Mathematical / Computational / Theoretical physics Books
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Categories in Continuum Physics: Lectures Given at a Workshop Held at SUNY, Buffalo 1982
Table of ContentsContinuum mechanics and geometric integration theory.- Structure of continuum physics.- On differentiable spaces.- Cartesian closed categories and analysis of smooth maps.- to synthetic differential geometry, and a synthetic theory of dislocations.- Synthetic reasoning and variable sets.- Recent research on the foundations of thermodynamics.- Global and local versions of the second law of thermodynamics.- Thermodynamics and the hahn-banach theorem.- What is the length of a potato?.
£24.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Theory of Nonlinear Lattices
Book SynopsisSoliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.Table of Contents1. Introduction.- 1.1 The Fermi-Pasta-Ulam Problem.- 1.2 Hénon-Heiles Calculation.- 1.3 Discovery of Solitons.- 1.4 Dual Systems.- 2. The Lattice with Exponential Interaction.- 2.1 Finding of an Integrable Lattice.- 2.2 The Lattice with Exponential Interaction.- 2.3 Periodic Solutions.- 2.4 Solitary Waves.- 2.5 Two-Soliton Solutions.- 2.6 Hard-Sphere Limit.- 2.7 Continuum Approximation and Recurrence Time.- 2.8 Applications and Extensions.- 2.9 Poincaré Mapping.- 2.10 Conserved Quantities.- 3. The Spectrum and Construction of Solutions.- 3.1 Matrix Formalism.- 3.2 Infinite Lattice.- 3.3 Scattering and Bound States.- 3.4 The Gel’fand-Levitan Equation.- 3.5 The Initial Value Problem.- 3.6 Soliton Solutions.- 3.7 The Relationship Between the Conserved Quantities and the Transmission Coefficient.- 3.8 Extensions of the Equations of Motion and the Kac-Moerbeke System.- 3.9 The Bäcklund Transformation.- 3.10 A Finite Lattice.- 3.11 Continuum Approximation.- 4. Periodic Systems.- 4.1 Discrete Hill’s Equation.- 4.2 Auxiliary Spectrum.- 4.3 Relation Between ?j (k) and ?j (0).- 4.4 Related Integrals on the Riemann Surface.- 4.5 Solution to the Inverse Problem.- 4.6 Time Evolution.- 4.7 A Simple Example (A Cnoidal Wave).- 4.8 Periodic System of Three-Particles.- 5. Application of the Hamilton-Jacobi Theory.- 5.1 Canonically Conjugate Variables.- 5.2 Action Variables.- 6. Recent Advances in the Theory of Nonlinear Lattices.- 6.1 The KdV Equation as a Limit of the TL Equation.- 6.2 Interacting Soliton Equations.- 6.3 Integrability.- 6.4 Generalization of the TL Equation.- 6.5 Two-Dimensional TL.- 6.6 Bethe Ansatz.- 6.7 The Thermodynamic Limit.- 6.8 Hierarchy of Nonlinear Equations.- 6.9 Some Numerical Results.- Appendices.- Simplified Answers to Main Problems.- References.- List of Authors Cited in Text.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Field Theory Handbook: Including Coordinate Systems, Differential Equations and Their Solutions
Book SynopsisLet us first state exactly what this book is and what it is not. It is a compendium of equations for the physicist and the engineer working with electrostatics, magne tostatics, electric currents, electromagnetic fields, heat flow, gravitation, diffusion, optics, or acoustics. It tabulates the properties of 40 coordinate systems, states the Laplace and Helmholtz equations in each coordinate system, and gives the separation equations and their solutions. But it is not a textbook and it does not cover relativistic and quantum phenomena. The history of classical physics may be regarded as an interplay between two ideas, the concept of action-at-a-distance and the concept of a field. Newton's equation of universal gravitation, for instance, implies action-at-a-distance. The same form of equation was employed by COULOMB to express the force between charged particles. AMPERE and GAUSS extended this idea to the phenomenological action between currents. In 1867, LUDVIG LORENZ formulated electrodynamics as retarded action-at-a-distance. At almost the same time, MAXWELL presented the alternative formulation in terms of fields. In most cases, the field approach has shown itself to be the more powerful.Table of ContentsI. Eleven coordinate systems.- II. Transformations in the complex plane.- III. Cylindrical systems.- IV. Rotational systems.- V. The vector Helmholtz equation.- VI. Differential equations.- VII. Functions.- Appendix. Symbols.- Author Index.
£113.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum-Classical Analogies
Book SynopsisIt is unanimously accepted that the quantum and the classical descriptions of the physical reality are very different, although any quantum process is "mysteriously" transformed through measurement into an observable classical event. Beyond the conceptual differences, quantum and classical physics have a lot in common. And, more important, there are classical and quantum phenomena that are similar although they occur in completely different contexts. For example, the Schrödinger equation has the same mathematical form as the Helmholtz equation, there is an uncertainty relation in optics very similar to that in quantum mechanics, and so on; the list of examples is very long. Quantum-classical analogies have been used in recent years to study many quantum laws or phenomena at the macroscopic scale, to design and simulate mesoscopic devices at the macroscopic scale, to implement quantum computer algorithms with classical means, etc. On the other hand, the new forms of light – localized light, frozen light – seem to have more in common with solid state physics than with classical optics. So these analogies are a valuable tool in the quest to understand quantum phenomena and in the search for new (quantum or classical) applications, especially in the area of quantum devices and computing.Trade ReviewFrom the reviews: "The main role of quantum classical analogies presented in ten distinct chapters is to shed some light on the genuine significance of the quantum and classical worlds. … The book addresses a large category of readers, especially graduates and PhD students … . The book is also useful for researchers working in advanced topics … . It can be used as an additional source for a course on quantum mechanics … . The hard cover book is nicely edited … ." (Roland Carchon, Physicalia, Vol. 57 (3), 2005) "The authors … devote their new book to the striking analogies between classical and quantum physics. … the authors wish to show that the classical and quantum worlds share many common concepts despite striking differences. … The wealth of analogies … discovered and presented in ten distinct chapters sheds some light on the genuine significance of both the quantum world and its classical counterpart. The book addresses students and researchers alike specialising in the study of quantum devices, atom optics or quantum optics." (Gert Roepstorff, Zentralblatt MATH, Vol. 1093 (19), 2006) "Analogies are a powerful cognitive tool that allow us to make inferences and learn new aspects from the comparison of two things by highlighting their similarities. … It is important to mention that the book is intended to be a catalogue of phenomena shared between classical and quantum physics … . the references given are an invaluable asset. … This book is therefore a very good choice for those interested in bridging ideas from classical physics into the quantum world or vice versa." (Dr. J. Rogel-Salazar, Contemporary Physics, Vol. 46 (6), 2005) "This book develops and explores in a systematic manner a large number of analogs between quantum and classical theories. … It follows closely the recent experimental developments, and for each chapter there is a large number of current references. … It will be very valuable for a large category of readers ranging from graduate and Ph. D. students to researchers working in these areas, and on to teachers looking for nontrivial modern applications and developments in both quantum and classical physics." (Vitor R. Vieira, Mathematical Reviews, Issue 2007 c)Table of Contents1 Introduction.- 2 Analogies Between Ballistic Electrons and Electromagnetic Waves.- 3 Electron/Electromagnetic Multiple Scattering and Localization.- 4 Acoustic Analogies for Quantum Mechanics.- 5 Optical Analogs for Multilevel Quantum Systems.- 6 Particle Optics.- 7 Quantum/Classical Nonlinear Phenomena.- 8 Quantum/Classical Phase Space Analogies.- 9 Analogies Between Quantum and Classical Computing.- 10 Other Quantum/Classical Analogies.- References.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Astronomie mit dem Personal Computer
Book SynopsisAstronomie mit dem PC vermittelt dem Leser eine fundierte Einführung in die Welt der himmelsmechanischen Berechnungen, die für die astronomische Beobachtungspraxis von besonderer Bedeutung sind.Von den theoretischen Grundlagen der Astronomie und Numerik bis zur Erstellung schneller und präziser Anwendungsprogramme vermittelt das Buch die notwendigen Kenntnisse und Softwarelösungen für die Bestimmung und Vorhersage von:- Positionen der Sonne, des Mondes und der Planeten- Auf- und Untergangszeiten- physischen Ephemeriden der Sonne und der großen Planeten- Kometen- und Kleinplanetenpositionen (mit Störungen)- Mondphasen- Zentrallinie und lokalen Umständen von Sonnenfinsternissen - Sternbedeckungen durch den Mond- Bahnelementen aus drei Beobachtungen (auch mehrere Lösungen)- Koordinaten aus Himmelsaufnahmen. Die Verwendung der weitverbreiteten objektorientierten Programmiersprache CC++ ermöglicht die effiziente Realisierung eigener Anwendungen auf der Basis einer leistungsfähigen Modul-Bibliothek. Die Begleit-CD enthält neben den vollständigen, ausgiebig dokumentierten und kommentierten Quelltexten auch die ausführbaren Programme - damit können Leser ohne Programmierkenntnisse alle im Buch beschriebenen Programme ebenfalls nutzen. Zusätzlich befinden sich zwei Sternkataloge (Position und Proper Motion Katalog und Zodialkatalog) sowie die Lowell-Datenbank aktueller Kleinplaneten-Bahnelemente auf der CD, die den Nutzwert der entsprechenden Programme weiter erhöhen. Die vorliegende 4. Auflage stellt, neben einigen Überarbeitungen der Texte und Bilder, die ausführbaren Programme für die Betriebssysteme Windows 98/2000/XP und LINUX sowie die akualisierten Kataloge und Datenbanken zur Verfügung.Table of ContentsEinführung.- Koordinatensysteme.- Auf- und Untergangsrechnung.- Kometenbahnen.- Störungsrechnung.- Planetenbahnen.- Physische Planetenephemeriden.- Die Mondbahn.- Sonnenfinsternisse.- Sternbedeckungen.- Bahnbestimmung.- Astrometrie.
£52.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
Book SynopsisHigh resolution upwind and centered methods are a mature generation of computational techniques. They are applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. For its third edition the book has been thoroughly revised to contain new material.Table of ContentsThe Equations of Fluid Dynamics.- Notions on Hyperbolic Partial Differential Equations.- Some Properties of the Euler Equations.- The Riemann Problem for the Euler Equations.- Notions on Numerical Methods.- The Method of Godunov for Non#x2014;linear Systems.- Random Choice and Related Methods.- Flux Vector Splitting Methods.- Approximate#x2014;State Riemann Solvers.- The HLL and HLLC Riemann Solvers.- The Riemann Solver of Roe.- The Riemann Solver of Osher.- High#x2013;Order and TVD Methods for Scalar Equations.- High#x2013;Order and TVD Schemes for Non#x2013;Linear Systems.- Splitting Schemes for PDEs with Source Terms.- Methods for Multi#x2013;Dimensional PDEs.- Multidimensional Test Problems.- FORCE Fluxes in Multiple Space Dimensions.- The Generalized Riemann Problem.- The ADER Approach.- Concluding Remarks.
£237.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Analysis 1
Book SynopsisDas vorliegende Lehrbuch ist als Leitfaden für eine zwei- oder dreisemestrige Analysis-Vorlesung gedacht und richtete sich an Studierende der Mathematik und Physik sowie an mathematisch interessierte Studierende der Informatik und der exakten Wissenschaften. Ausführliche Beweise und Erläuterungen sowie zahlreiche Beispiele und interessante Übungsaufgaben eignen es sehr gut für das mathematische Selbststudium. Ein klarer und übersichtlicher Aufbau und eine geschickte Gliederung des Stoffes ermöglichen, das erste Studium auf Kernbereiche zu beschränken. Dem Dozenten werden vielfältige Möglichkeiten geboten, je nach Art der Vorlesung verschiedene Schwerpunkte zu setzen und geeignete Wege zur Darstellung des Stoffes zu wählen. Geometrische Intuition und historische Motivation in Verbindung mit einer maßvollen Abstraktion kennzeichnen diese moderne Einführung in die Analysis.Trade ReviewAus den Rezensionen zur 2. Auflage: "… Genauigkeit und Verständlichkeit schliessen sich nicht aus, wie das Buch von Stefan Hildebrand eindrücklich zeigt. Der Stoff wird übersichtlich, detailliert und genau präsentiert. … Das vorliegende Werk präsentiert … in hervorragender Weise - quasi als Referenzwerk. … Ich hätte mir als Studierender gewünscht ein solches Buch zu besitzen. Ich würde es deshalb auch allen (ehemaligen) Schülerinnen und Schüler, die sich ernsthaft für Mathematik interessieren, empfehlen." (Reto Schuppli, in: Bulletin des Verein Schweizer Mathematik- und Physiklehrer, 2006, S. 21) Aus den Rezensionen zur 2. Auflage: "… eindrucksvoll ... Meisterhaft gelingt hier die Synthese vielschichtiger, vielfältiger, … klaren, übersichtlichen, gut strukturiertem Aufbau … einem überzeugenden, von üblichen Lehrbüchern grundsätzlich abweichenden Konzept. …aus didaktischer Sicht sehr wertvoll … Beispiele und wertvolle Übungsaufgaben, bei maßvoller Abstraktion, besonders auf geometrische Intuition und historische Motivation Wert gelegt wird, eignet sich dieses Buch sehr gut zum … Selbststudium und bietet dem Dozenten eine Fülle von Anregungen für eine zumindest zweisemestrige Vorlesung." (H. Rindler, in: Monatshefte für Mathematik, 2006, Vol. 149, S. 85) "… Hildebrandts Werk ist ein empfehlenswertes Werk … Der kenntnisreiche Autor zeigt, dass er auch Geschmack hat! … Die Auswahl des Stoffes ... ist subjektiv gefärbt, aber in sich stimmig. … Ein sehr gefälliges und empfehlenswertes Buch: Für die Studenten als Begleitlektüre oder zum Selbststudium, und für die Dozenten … als Grundlage … von Grundvorlesungen!" (H. Prodinger, in: IMN - Internationale Mathematische Nachrichten, 2007, Vol. 205, S. 42)Table of ContentsDie Grundlagen der Analysis.- Der Begriff der Stetigkeit.- Grundbegriffe der Differential- und Integralrechnung.- Differentialgleichungen und Fourierreihen.
£38.48
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Open Quantum Systems I: The Hamiltonian Approach
Book SynopsisUnderstanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.Table of Contentsto the Theory of Linear Operators.- to Quantum Statistical Mechanics.- Elements of Operator Algebras and Modular Theory.- Quantum Dynamical Systems.- The Ideal Quantum Gas.- Topics in Spectral Theory.
£52.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Group Theory: Application to the Physics of
Book SynopsisThis concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.Trade ReviewFrom the reviews:"It was developed for a graduate course taught mostly by Millie Dresselhaus at MIT for more than 30 years, with many revisions of lecture notes. Very much a graduate text or specialist monograph, the book covers a wealth of applications across solid-state physics. … The book can be warmly recommended to students and researchers in solid-state physics, either to serve as a text for an advanced lecture course or for individual study … ." (Volker Heine, Physics Today, November, 2008)"This textbook is based on the authors’ pedagogical experience during their 30 years at MIT. … the book develops all of the relevant mathematics (linear algebra) and the necessary physics (quantum mechanics), it is eminently suitable to a wide audience in physics, chemistry and materials science." (Barry R. Masters, Optics and Photonics News, July/August, 2009)“This is an excellent text … . originates from lectures by Charles Kittel and J. H. van Vleck in the 1950s and much of the material was presented in courses by the authors over the last three decades. The material is meant for Electrical Engineering and Physics students at the graduate level … . has exercises at the end of each chapter and an extensive set of appendices. The exposition is clear and detailed. This is a very good book for its target audience.” (W. Miller Jr., Zentralblatt MATH, Vol. 1175, 2010)“The goal of the book under review is to teach group theory in close connection to applications. … Every chapter of the book finishes with several selected problems. Specific to this book is the feature that every abstract theoretical group concept is introduced and applied in a concrete physical way. This is why the book is very useful for anyone interested in applications of group theory to the wide range of condensed matter phenomena.” (Oktay K. Pashaev, Mathematical Reviews, Issue 2010 i)“It is highly welcomed because of its well-thought structuring and the plenty of non-trivial examples. The authors develop those parts of the theory of groups which are interesting for physicists, from chapter to chapter offering nearly at any step one or more informative application.” (G. Kowol, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)Table of ContentsBasic Mathematics.- Basic Mathematical Background: Introduction.- Representation Theory and Basic Theorems.- Character of a Representation.- Basis Functions.- Introductory Application to Quantum Systems.- Splitting of Atomic Orbitals in a Crystal Potential.- Application to Selection Rules and Direct Products.- Molecular Systems.- Electronic States of Molecules and Directed Valence.- Molecular Vibrations, Infrared, and Raman Activity.- Application to Periodic Lattices.- Space Groups in Real Space.- Space Groups in Reciprocal Space and Representations.- Electron and Phonon Dispersion Relation.- Applications to Lattice Vibrations.- Electronic Energy Levels in a Cubic Crystals.- Energy Band Models Based on Symmetry.- Spin–Orbit Interaction in Solids and Double Groups.- Application of Double Groups to Energy Bands with Spin.- Other Symmetries.- Time Reversal Symmetry.- Permutation Groups and Many-Electron States.- Symmetry Properties of Tensors.
£56.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Ordinary Differential Equations
Book SynopsisFew books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEWTrade ReviewFrom the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation … . The new edition is highly recommended as a general reference for the essential theory of ordinary differential equations and as a textbook for an introductory course for serious undergraduate or graduate students. … In the US system, it is an excellent text for an introductory graduate course." (Carmen Chicone, SIAM Review, Vol. 49 (2), 2007) "Vladimir Arnold’s is a master, not just of the technical realm of differential equations but of pedagogy and exposition as well. … The writing throughout is crisp and clear. … Arnold’s says that the book is based on a year-long sequence of lectures for second-year mathematics majors in Moscow. In the U.S., this material is probably most appropriate for advanced undergraduates or first-year graduate students." (William J. Satzer, MathDL, August, 2007)Table of ContentsBasic Concepts.- Basic Theorems.- Linear Systems.- Proofs of the Main Theorems.- Differential Equations on Manifolds.
£58.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Bryce DeWitt's Lectures on Gravitation: Edited by Steven M. Christensen
Book SynopsisBryce DeWitt, a student of Nobel Laureate Julian Schwinger, was himself one of the towering figures in 20th century physics, particularly renowned for his seminal contributions to quantum field theory, numerical relativity and quantum gravity. In late 1971 DeWitt gave a course on gravitation at Stanford University, leaving almost 400 pages of detailed handwritten notes. Written with clarity and authority, and edited by his former student Steven Christensen, these timeless lecture notes, containing material or expositions not found in any other textbooks, are a gem to be discovered or re-discovered by anyone seriously interested in the study of gravitational physics.Trade ReviewFrom the reviews:“DeWitt’s lectures cover interesting and detailed material which is rarely found in other text books. It is a book for the advanced reader.” (Norbert Dragon, General Relativity and Gravitation, Vol. 44, 2012)Table of ContentsReview of the Uses of Invariants in Special Relativity.- Accelerated Motion in Special Relativity.- Realization of Continuous Groups.- Riemannian Manifolds.- The Free Particle Geodesics.- Weak Field Approximation. Newton`s Theory.- Ensembles of Particles.- Production of Gravitational Fields by Matter.- Conservation Laws.- Phenomenological Description of a Conservative Continuous Medium.- Solubility of the Einstein and Matter Equations.- Energy, Momentum and Stress in the Gravitational Field.- Measurement of Asymptotic Field.- The Electromagnetic Field.- Gravitational Waves.- Spinning Bodies.- Weak Field Gravitational Wave.- Stationary Spherically (or Rotationally) Symmetric Metric.- Kerr Metric Subcalculations.- Friedmann Cosmology.- Dynamical Equations and Diffeomorphisms.
£61.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Lectures on Partial Differential Equations
Book SynopsisChoice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.Trade ReviewFrom the reviews of the German edition: "This book provides an introductory text (in German) to basic partial differential equations, based on the author's lectures at Moscow University. […] Most of the standard themes are treated (see list below), but some unusual topics are covered as well. For instance, in chapter 10 double layer potentials are considered, and chapters 11 and 13 deal (among others) with Maxwell's theorem on the multipole expansion of spherical functions. The style of the book is quite non-technical (it contains almost no estimates), taking a mainly geometric viewpoint. [...]" Markus Kunze, Zentralblatt für Mathematik 1076.35001 From the reviews: "[...] This excellent and stimulating textbook gives a beautiful first view on some basic aspects of the theory of partial differential equations and can be warmly recommended to any graduate student in mathematics and physics." M.Günther, Zeitschrift für Angewandte Analysis und Ihre Anwendungen, Vol. 24, Issue 4, 2005 "…..Arnold .. has long held a reputation as one of the world's leaders in dynamics and geometry. His Lectures survey big ideas; accordingly, he largely suppresses both the functional analytic formalism and the delicate estimates so characteristic of the subject. He takes the viewpoint that the most important PDEs arise in physics and the most important mathematical ideas contributing to their solution derive from physical principles. Amold concentrates on the simplest equations of a given type and shows how the key ideas play out. For example, he attacks the general theory of one first-order equation, first via wave-particle duality, then via Hamiltonian dynamics. .... The author's stature and the book's lucidity make this an essential acquisition for all College libraries. …." D.V.Feldman, CHOICE, January 2005 Vol. 42 No. 05 "... Professor Arnold's Lectures on Partial Differential Equations is an ambitious, intensely personal effort to reconnect the subject with some of its roots in modeling physical processes. He does so in a lively lecture-style format, resulting in a book that would complement almost any course in PDEs. ... As can be gleaned from the previous paragraph, we bouth found the book by V.I.Arnold most stimulating and thought provoking, leading to statements such as, "It has been years since I enjoyed a book so much" by RBG and "I cannot point to any other book in mathematics written with the same intensity" by EAT. ... ... what follows [...] is a beautiful book on PDEs, interwoven with the exposition of deep physical, geometrical, and topological insights that contribute to both the understanding and history of PDEs. Prof. Arnold's book ... connects with the roots of the field and brings in concepts from geometry, continuum mechanics, and analysis. It can be used together with any book on PDEs and students will welcome its directness and freshness. We know of no other book like it on the market and highly recommend it for individual reading and as an accompaniment to any course in PDEs. ..." R.B. Guenther, E.A.Thomann, SIAM Review, Vol. 47, No. 1, 2005 "This book contains the transcripts of twelve lectures on partial differential equations … . The presentation gives a vivid sense of what was actually said and discussed in the lecture course, and in this fashion the book differs markedly from many text books with similar titles. … The author uses physical intuition to derive the various mathematical theories, and is thus able to explain the ideas … in a fashion which is clear and helpful to both novice and expert." M. Groves, ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 85 (4), 2005 "[...] In brief, this book contains beautifully structured lectures on classical theory of linear partial differential equations of mathematical physics. Professor Arnold stresses the importance of physical intuitions and offers in his lecture a deep geometric insight into these equations. The book is highly recommended to anybody interested in partial differential equations as well as those involved in lecturing on these topics. I encourage readers of this book to take note of the Preface which contains very interesting comments on the role of Bourbaki's group in mathematics, a theme which resurfaces many times in these lectures." J.Chabrowski, Gazette, Australian Mathematical Society, Vol. 31, Issue 5, 2004 "... As a result the author has aimed to impart to students with pre-knowledge of only a basic kind (linear algebra, basic analysis, ordinary differential equations, ...) the essence of the theory and applications of the subject of partial differential equations. Of course the subject is fundamental in mathematics and in physics and the author is an evangelist for keeping the subject mainstream for mathematicians and for physicists. He has attempted, he writes, to adhere to the principle of minimal generality, according to which every idea should first be clearly understood in the simplest situation! This is successfully done, so that this book should prove attractive in length and in scope to its target readership. ... In this new excellent text are included a large number of interesting problems; at the end of the book there is a full set of problems from examinations given in Moscow. ..." F.H.Berkshire, Imperial College London, Contemporary Physics 2004, Vol. 45, Issue 6 "Like all Vladimir Arnold’s books, this one is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject … . A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging!" L’Enseignement Mathematique, Vol. 50 (1-2), 2004 "Dieses Buch betont geometrische Einsicht und physikalische Intuition. Die Prinzipien werden an Bildern erläutert, und das Buch enthält mehr Text als Formeln und Sätze. […]. Neben einer großen Anzahl von Übungsaufgaben, die im Buch verstreut sind, finden sich interessante Prüfungsbeispiele der Moskauer Universität." J. Hertling, Internationale Mathematische Nachrichten, 2004, Issue 197, p. 47-48 "The book is based on a short course of lectures delivered to the third year mathematics students of the Independent University of Moscow … . The book can serve as a nonstandard, geometrically motivated introduction to PDEs for students … . It is, probably, worth mentioning that the introduction contains some general philosophical views of the author on the subject of PDEs and modern mathematics as a whole and will be of interest to a broad mathematical audience." (Victor Shubov, MathDL, January, 2001) "Like other books of Arnold, this is a very original introduction to the subject. It is … based on a course delivered to third-year students of mathematics. The aim of this book is to teach the fundamental ideas of partial differential equations and mathematical physics. … Not only students but also professional mathematicians from other fields of mathematics can learn the basic and simple ideas of partial differential equations from this unique book." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 74, 2008)Table of Contents1. The General Theory for One First-Order Equation.- 2. The General Theory for One First-Order Equation (Continued).- 3. Huygens’ Principle in the Theory of Wave Propagation.- 4. The Vibrating String (d’Alembert’s Method).- 5. The Fourier Method (for the Vibrating String).- 6. The Theory of Oscillations. The Variational Principle.- 7. The Theory of Oscillations. The Variational Principle (Continued).- 8. Properties of Harmonic Functions.- 9. The Fundamental Solution for the Laplacian. Potentials.- 10. The Double-Layer Potential.- 11. Spherical Functions. Maxwell’s Theorem. The Removable Singularities Theorem.- 12. Boundary-Value Problems for Laplace’s Equation. Theory of Linear Equations and Systems.- A. The Topological Content of Maxwell’s Theorem on the Multifield Representation of Spherical Functions.- A.1. The Basic Spaces and Groups.- A.2. Some Theorems of Real Algebraic Geometry.- A.3. From Algebraic Geometry to Spherical Functions.- A.4. Explicit Formulas.- A.6. The History of Maxwell’s Theorem.- Literature.- B. Problems.- B.1. Material from the Seminars.- B.2. Written Examination Problems.
£52.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Mechanics: Symbolism of Atomic Measurements
Book SynopsisA unique legacy, these lecture notes of Schwinger’s course held at the University of California at Los Angeles were carefully edited by his former collaborator Berthold-Georg Englert and constitute both a self-contained textbook on quantum mechanics and an indispensable source of reference on this fundamental subject by one of the foremost thinkers of twentieth century physics.Trade ReviewFrom the reviews: "Quantum Mechanics: Symbolism of Atomic Measurements is not just another textbook on quantum mechanics. Rather, it contains truly novel elements of both content and style. In particular, Schwinger begins his treatment not with de Broglie waves or the Schrödinger equation but rather with the measurement process. His idea is to derive, or at least make plausible, the formalism of state vectors, bras and kets, by reference to quantum measurements such as the Stern-Gerlach experiment. This [...] is simply the basis of a new way of teaching quantum mechanics. This opening chapter should be of interest to all scholars of quantum theory and might form a new topic of research for philosophers of quantum mechanics." (Contemporary Physics, 44/2, 2003) "There are dozen of excellent textbooks on the market. But this one really is different." (T. Kibble, The Times Higher Education Supplement, 2001) "The material covered is superficially similar to that of a typical graduate quantum mechanics course [...] However, each chapter has beautiful and unusual treatments of familiar topics. [...] This book would make an outstanding supplement and reference for a graduate quantum mechanics course. Theoretical physicists will delight in this wonderful book, which should be available in the library system of any institution with a research or graduate program in physics. Graduate students through professionals." (CHOICE, Dec. 2001) "The book is a tour-de-force. Once the groundwork is laid, he goes into subjects with the mathematical virtuosity for which he was famous – not advanced mathematics, but the incredible use of simple mathematics. … there are gems throughout the book. … it is a wonderful book for a professor to own, like Feyman’s lectures, because there is so much to learn from it. … The book was lovingly edited from some UCLA lecture notes, by Berthold-Georg Englert, a longtime student and assistant of Schwinger’s … ." (Daniel Greenberger, American Journal of Physics, Vol 71 (9), 2003) "Editor Englert has performed a service for physicists everywhere by making available this book, which is based on Schwinger’s unpublished UCLA lecture notes. … each chapter has beautiful and unusual treatments of familiar topics. … There are excellent problems at the end of each chapter. This book would make an outstanding supplement and reference for a graduate quantum mechanics course. Theoretical physicists will delight in this wonderful book, which should be available in the library system of any institution with a research or graduate program … ." (M. C. Ogilvie, CHOICE, December, 2001) "The book commences with an absorbing prologue in which Schwinger talks us through the development of quantum mechanic and quantum field theory in an easy conversational style. … The book is packed with exercises for the reader to attempt. … Anyone who works religiously through these exercises will acquire a thoroughly adequate command of quantum mechanics." (W. Cox, Mathematical Reviews, Issue 2002 h) "Quantum mechanics: Symbolism of Atomic Measurements is not just another textbook on quantum mechanics. Rather, it contains truly novel elements of both content and style. … This opening chapter should be of interest to all scholars of quantum theory and might form a new topic of research for philosophers of quantum mechanics. Throughout the text, new material is presented at a breathless pace. All the usual elements of the subject are there, but Schwinger’s presentation reveals surprises in even the most familiar of these." (S. M. Barnett, Contemporary Physics, Vol. 44 (2), 2003) "In the beginning, the editor has added an important material in the form of a prologue … . This is one of the best treatments of the philosophy of quantum mechanics, which I have come across. … One of the major features of the book is the incorporation of a large number of problems … . the contents of the problems are well integrated in the text and have become part of it. This has caused a rich and tight structure of the logical arguments." (S. S. Bhattacharyya, Indian Journal of Physics, Vol. 76B (3), 2002) "This unique textbook is based upon the lecture notes that Julian Schwinger wrote up for the students of the quantum mechanics course … . this book would probably make an ideal quantum mechanics reference … . There are a large number of problems included at the end of each chapter, which comprise an excellent resource for any lecturer … . this textbook is a unique resource, which provides an insight into the thoughts and deliberations of one of this century’s giants of quantum mechanics." (P. C. Dastoor, The Physicist, Vol. 38 (5), 2001) "There are dozens of excellent textbooks on the market. But this one really is different. … there is a carefully argued historical and philosophical prologue that sets the scene, centred on the two key features of quantum physics – atomicity and its probabilistic character; this alone would make the book worthwhile. The emphasis on discrete variables is a very modern approach… . To a theoretical physicist, this book is a delight and a wonderful resource. … This is a book I shall treasure." (Tom Kibble, Times Higher Education Supplement, September, 2001)Table of ContentsPrologue.- A. Fall Quarter: Quantum Kinematics.- 1 Measurement Algebra.- 2 Continuous q, p Degree of Freedom.- 3 Angular Momentum.- 4 Galilean Invariance.- B. Winter Quarter: Quantum Dynamics.- 5 Quantum Action Principle.- 6 Elementary Applications.- 7 Harmonic Oscillators.- 8 Hydrogenic Atoms.- C. Spring Quarter: Interacting Particles.- 9 Two-Particle Coulomb Problem.- 10 Identical Particles.- 11 Many-Electron Atoms.- 12 Electromagnetic Radiation.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Theory of Operator Algebras I
Book SynopsisSince its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.Trade Review"... These three bulky volumes [EMS 124, 125, 127], written by one of the most prominent researchers of the area, provide an introduction to this repidly developing theory. ... These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of matematics. Furthermore, they should be on the bookshelf of every researcher of the area." (László Kérchy, Acta Scientiarum Mathematicarum, Vol. 69, 2003)Table of ContentsFundaments of Banach Algebras and C*-Algebras.- Topologies and Density Theorems in Operator Algebras.- Conjugate Spaces.- Tensor Products of Operator Algebras and Direct Integrals.- Types of von Neumann Algebras and Traces.- Appendix: Polish Spaces and Standard Borel Spaces.
£151.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Mathematical Physics: Atoms, Molecules and Large Systems
Book SynopsisThis book is a new edition of Volumes 3 and 4 of Walter Thirring’s famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions.Trade ReviewFrom the reviews of the second edition: "Just as the general theory of relativity leads to many new mathematical advances and applications, the same is true of quantum mechanics. It is these mathematical advances that are the topic of this extensive volume, a volume which also delineates how these advances made possible the difficult transition from understanding hydrogen to understanding complex atoms, molecules, and ‘large systems’. As such this volume will serve as an excellent source book for the mathematical basis of the many recent advances in quantum mechanics. It will also serve as an excellent text book for an advanced course in either quantum physics or applied mathematics." (Physicalia, 25/3, 2003) "This work is written uncompromisingly for the mathematical physicist … . Thirring writes concisely but with a clarity that makes the book easy to read. … There are extensive bibliographies, with references mostly to articles in journals … . There are copious problems and–even better-all the solutions. … the volume would make a valuable addition to the library of … a mathematical physicist." (Prof. A.I. Solomon, Contemporary Physics, Vol. 46 (4), 2005) "This volume will serve as an excellent source book for the mathematical basis of the many recent advances in quantum mechanics. It will also serve as an excellent textbook … . Each chapter is chock full of mathematical derivations and proofs but perhaps the most interesting part of each proof is the following section entitled ‘Remarks’ sections which are full of interesting details, ideas, drawbacks, comments, and references. … As is usually the case with Springer-Verlag, this book has been beautifully produced … ." (Fernande Grandjean and Gary J. Long, Physicalia, Vol. 25 (3), 2003)Table of ContentsI Quantum Mechanics of Atoms and Molecules.- 1 Introduction.- 2 The Mathematical Formulation of Quantum Mechanics.- 3 Quantum Dynamics.- 4 Atomic Systems.- II Quantum Mechanics of Large Systems.- 1 Systems with Many Particles.- 2 Thermostatics.- 3 Thermodynamics.- 4 Physical Systems.- Bibliography to Part I.- Bibliography to Part II.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Spectral Methods in Fluid Dynamics
Book SynopsisThis is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.Table of Contents1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.2.1. A Fourier Galerkin Method for the Wave Equation.- 1.2.2. A Chebyshev Collocation Method for the Heat Equation.- 1.2.3. A Legendre Tau Method for the Poisson Equation.- 1.2.4. Basic Aspects of Galerkin, Tau and Collocation Methods.- 1.3. The Equations of Fluid Dynamics.- 1.3.1. Compressible Navier-Stokes.- 1.3.2. Compressible Euler.- 1.3.3. Compressible Potential.- 1.3.4. Incompressible Flow.- 1.3.5. Boundary Layer.- 1.4. Spectral Accuracy for a Two-Dimensional Fluid Calculation.- 1.5. Three-Dimensional Applications in Fluids.- 2. Spectral Approximation.- 2.1. The Fourier System.- 2.1.1. The Continuous Fourier Expansion.- 2.1.2. The Discrete Fourier Expansion.- 2.1.3. Differentiation.- 2.1.4. The Gibbs Phenomenon.- 2.2. Orthogonal Polynomials in ( — 1, 1).- 2.2.1. Sturm—Liouville Problems.- 2.2.2. Orthogonal Systems of Polynomials.- 2.2.3. Gauss-Type Quadratures and Discrete Polynomial Transforms.- 2.3. Legendre Polynomials.- 2.3.1. Basic Formulas.- 2.3.2. Differentiation.- 2.4. Chebyshev Polynomials.- 2.4.1. Basic Formulas.- 2.4.2. Differentiation.- 2.5. Generalizations.- 2.5.1. Jacobi Polynomials.- 2.5.2. Mapping.- 2.5.3. Semi-Infinite Intervals.- 2.5.4. Infinite Intervals.- 3. Fundamentals of Spectral Methods for PDEs.- 3.1. Spectral Projection of the Burgers Equation.- 3.1.1. Fourier Galerkin.- 3.1.2. Fourier Collocation.- 3.1.3. Chebyshev Tau.- 3.1.4. Chebyshev Collocation.- 3.2. Convolution Sums.- 3.2.1. Pseudospectral Transform Methods.- 3 2 2 Aliasing Removal by Padding or Truncation.- 3.2.3. Aliasing Removal by Phase Shifts.- 3.2.4. Convolution Sums in Chebyshev Methods.- 3.2.5. Relation Between Collocation and Pseudospectral Methods.- 3.3. Boundary Conditions.- 3.4. Coordinate Singularities.- 3.4.1. Polar Coordinates.- 3.4.2. Spherical Polar Coordinates.- 3.5. Two-Dimensional Mapping.- 4. Temporal Discretization.- 4.1. Introduction.- 4.2. The Eigenvalues of Basic Spectral Operators.- 4.2.1. The First-Derivative Operator.- 4.2.2. The Second-Derivative Operator.- 4.3. Some Standard Schemes.- 4.3.1. Multistep Schemes.- 4.3.2. Runge—Kutta Methods.- 4.4. Special Purpose Schemes.- 4.4.1. High Resolution Temporal Schemes.- 4.4.2. Special Integration Techniques.- 4.4.3. Lerat Schemes.- 4.5. Conservation Forms.- 4.6. Aliasing.- 5. Solution Techniques for Implicit Spectral Equations.- 5.1. Direct Methods.- 5.1.1. Fourier Approximations.- 5.1.2. Chebyshev Tau Approximations.- 5.1.3. Schur-Decomposition and Matrix-Diagonalization.- 5.2. Fundamentals of Iterative Methods.- 5.2.1. Richardson Iteration.- 5.2.2. Preconditioning.- 5.2.3. Non-Periodic Problems.- 5.2.4. Finite-Element Preconditioning.- 5.3. Conventional Iterative Methods.- 5.3.1. Descent Methods for Symmetric, Positive-Definite Systems.- 5.3.2. Descent Methods for Non-Symmetric Problems.- 5.3.3. Chebyshev Acceleration.- 5.4. Multidimensional Preconditioning.- 5.4.1. Finite-Difference Solvers.- 5.4.2. Modified Finite-Difference Preconditioners.- 5.5. Spectral Multigrid Methods.- 5.5.1. Model Problem Discussion.- 5.5.2. Two-Dimensional Problems.- 5.5.3. Interpolation Operators.- 5.5.4. Coarse-Grid Operators.- 5.5.5. Relaxation Schemes.- 5.6. A Semi-Implicit Method for the Navier—Stokes Equations.- 6. Simple Incompressible Flows.- 6.1. Burgers Equation.- 6.2. Shear Flow Past a Circle.- 6.3. Boundary-Layer Flows.- 6.4. Linear Stability.- 7. Some Algorithms for Unsteady Navier—Stokes Equations.- 7.1. Introduction.- 7.2. Homogeneous Flows.- 7.2.1. A Spectral Galerkin Solution Technique.- 7.2.2. Treatment of the Nonlinear Terms.- 7.2.3. Refinements.- 7.2.4. Pseudospectral and Collocation Methods.- 7.3. Inhomogeneous Flows.- 7.3.1. Coupled Methods.- 7.3.2. Splitting Methods.- 7.3.3. Galerkin Methods.- 7.3.4. Other Confined Flows.- 7.3.5. Unbounded Flows.- 7.3.6. Aliasing in Transition Calculations.- 7.4. Flows with Multiple Inhomogeneous Directions.- 7.4.1. Choice of Mesh.- 7.4.2. Coupled Methods.- 7.4.3. Splitting Methods.- 7.4.4. Other Methods.- 7.5. Mixed Spectral/Finite-Difference Methods.- 8. Compressible Flow.- 8.1. Introduction.- 8.2. Boundary Conditions for Hyperbolic Problems.- 8.3. Basic Results for Scalar Nonsmooth Problems.- 8.4. Homogeneous Turbulence.- 8.5. Shock-Capturing.- 8.5.1. Potential Flow.- 8.5.2. Ringleb Flow.- 8.5.3. Astrophysical Nozzle.- 8.6. Shock-Fitting.- 8.7. Reacting Flows.- 9. Global Approximation Results.- 9.1. Fourier Approximation.- 9.1.1. Inverse Inequalities for Trigonometric Polynomials.- 9.1.2. Estimates for the Truncation and Best Approximation Errors.- 9.1.3. Estimates for the Interpolation Error.- 9.2. Sturm—Liouville Expansions.- 9.2.1. Regular Sturm—Liouville Problems.- 9.2.2. Singular Sturm—Liouville Problems.- 9.3. Discrete Norms.- 9.4. Legendre Approximations.- 9.4.1. Inverse Inequalities for Algebraic Polynomials.- 9.4.2. Estimates for the Truncation and Best Approximation Errors.- 9.4.3. Estimates for the Interpolation Error.- 9.5. Chebyshev Approximations.- 9.5.1. Inverse Inequalities for Polynomials.- 9.5.2. Estimates for the Truncation and Best Approximation Errors.- 9.5.3. Estimates for the Interpolation Error.- 9.5.4. Proofs of Some Approximation Results.- 9.6. Other Polynomial Approximations.- 9.6.1. Jacobi Polynomials.- 9.6.2. Laguerre and Hermite Polynomials.- 9.7. Approximation Results in Several Dimensions.- 9.7.1. Fourier Approximations.- 9.7.2. Legendre Approximations.- 9.7.3. Chebyshev Approximations.- 9.7.4. Blended Fourier and Chebyshev Approximations.- 10. Theory of Stability and Convergence for Spectral Methods.- 10.1. The Three Examples Revisited.- 10.1.1. A Fourier Galerkin Method for the Wave Equation.- 10.1.2. A Chebyshev Collocation Method for the Heat Equation.- 10.1.3. A Legendre Tau Method for the Poisson Equation.- 10.2. Towards a General Theory.- 10.3. General Formulation of Spectral Approximations to Linear Steady Problems.- 10.4. Galerkin, Collocation and Tau Methods.- 10.4.1. Galerkin Methods.- 10.4.2. Tau Methods.- 10.4.3. Collocation Methods.- 10.5. General Formulation of Spectral Approximations to Linear Evolution Equations.- 10.5.1. Conditions for Stability and Convergence: The Parabolic Case.- 10.5.2. Conditions for Stability and Convergence: The Hyperbolic Case.- 10.6. The Error Equation.- 11. Steady, Smooth Problems.- 11.1. The Poisson Equation.- 11.1.1. Legendre Methods.- 11.1.2. Chebyshev Methods.- 11.1.3. Other Boundary Value Problems.- 11.2. Advection-Diffusion Equation.- 11.2.1. Linear Advection-Diffusion Equation.- 11.2.2. Steady Burgers Equation.- 11.3. Navier—Stokes Equations.- 11.3.1. Compatibility Conditions Between Velocity and Pressure.- 11.3.2. Direct Discretization of the Continuity Equation: The “inf-sup” Condition.- 11.3.3. Discretizations of the Continuity Equation by an Influence-Matrix Technique: The Kleiser—Schumann Method.- 11.3.4. Navier—Stokes Equations in Streamfunction Formulation.- 11.4. The Eigenvalues of Some Spectral Operators.- 11.4.1. The Discrete Eigenvalues for Lu = ? uxx.- 11.4.2. The Discrete Eigenvalues for Lu = ? vuxx + bux.- 11.4.3. The Discrete Eigenvalues for Lu = ux.- 12. Transient, Smooth Problems.- 12.1. Linear Hyperbolic Equations.- 12.1.1. Periodic Boundary Conditions.- 12.1.2. Non-Periodic Boundary Conditions.- 12.1.3. Hyperbolic Systems.- 12.1.4. Spectral Accuracy for Non-Smooth Solutions.- 12.2. Heat Equation.- 12.2.1. Semi-Discrete Approximation.- 12.2.2. Fully Discrete Approximation.- 12.3. Advection-Diffusion Equation.- 12.3.1. Semi-Discrete Approximation.- 12.3.2. Fully Discrete Approximation.- 13. Domain Decomposition Methods.- 13.1. Introduction.- 13.2. Patching Methods.- 13.2.1. Notation.- 13.2.2. Discretization.- 13.2.3. Solution Techniques.- 13.2.4. Examples.- 13.3. Variational Methods.- 13.3.1. Formulation.- 13.3.2. The Spectral-Element Method.- 13.4. The Alternating Schwarz Method.- 13.5. Mathematical Aspects of Domain Decomposition Methods.- 13.5.1. Patching Methods.- 13.5.2. Equivalence Between Patching and Variational Methods.- 13.6. Some Stability and Convergence Results.- 13.6.1. Patching Methods.- 13.6.2. Variational Methods.- Appendices.- A. Basic Mathematical Concepts.- B. Fast Fourier Transforms.- C. Jacobi—Gauss—Lobatto Roots.- References.
£71.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Symmetries in Physics: Group Theory Applied to Physical Problems
Book SynopsisSymmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.Table of Contents1. Introduction.- 2. Elements of the Theory of Finite Groups.- 2.1 Symmetry and Group Concepts: A Basic Example.- 2.2 General Theorems on Group Theory.- 2.3 Conjugacy Classes.- 3. Discrete Symmetry Groups.- 3.1 Point Groups.- 3.1.1 Symmetry Elements.- 3.1.2 Proper Point Groups.- 3.1.3 Improper Point Groups.- 3.2 Colour Groups and Magnetic Groups.- 3.3 Double Groups.- 3.4 Lattices, the Translation Group and Space Group.- 3.4.1 Normal Space Groups.- 3.4.2 Colour and Magnetic Space Groups.- 3.4.3 Double Space Groups.- 3.5 Permutation Groups.- 3.6 Other Finite Groups.- 4. Representations of Finite Groups.- 4.1 Linear Spaces and Operators.- 4.1.1 Linear and Unitary Spaces.- 4.1.2 Linear Operators.- 4.1.3 Special Operators and Eigenvalues.- 4.2 Introduction to the Theory of Representations.- 4.2.1 Operator Representations by Matrices.- 4.2.2 Equivalent Representations and Characters.- 4.2.3 Reducible and Irreducible Representations.- 4.2.4 Orthogonality Theorems.- 4.2.5 Subduction. Reality of Representations.- 4.3 Group Algebra.- 4.3.1 The Regular Representation.- 4.3.2 Projection Operators.- 4.4 Direct Products.- 4.4.1 Representations of Direct Products of Groups.- 4.4.2 The Inner Direct Product of Representations of a Group. Clebsch-Gordan Expansion.- 4.4.3 Simply Reducible Groups.- 5. Irreducible Representations of Special Groups.- 5.1 Point and Double Point Groups.- 5.2 Magnetic Point Groups. Time Reversal.- 5.3 Translation Groups.- 5.4 Permutation Groups.- 5.5 Tensor Representations.- 5.5.1 Tensor Transformations. Irreducible Tensors.- 5.5.2 Induced Representations.- 5.5.3 Irreducible Tensor Spaces.- 5.5.4 Direct Products and Their Reduction.- 6. Tensor Operators and Expectation Values.- 6.1 Tensors and Spinors.- 6.2 The Wigner-Eckart Theorem.- 6.3 Eigenvalue Problems.- 6.4 Perturbation Calculus.- 7. Molecular Spectra.- 7.1 Molecular Vibrations.- 7.1.1 Equation of Motion and Symmetry.- 7.1.2 Determination of Eigenvalues and Eigenvectors.- 7.1.3 Selection Rules.- 7.2 Electron Functions and Spectra.- 7.2.1 Symmetry in Many-Particle Systems.- 7.2.2 Symmetry-Adapted Atomic and Molecular Orbitals.- 7.2.3 The Hückel Method and Ligand Field Theory.- 7.3 Many-Electron Problems.- 7.3.1 Permutation Symmetry.- 7.3.2 Point and Permutation Symmetry. Molecular States.- 7.3.3 The H2 Molecule.- 8. Selection Rules and Matrix Elements.- 8.1 Selection Rules of Tensor Operators.- 8.2 The Jahn-Teller Theorem.- 8.2.1 Spinless States.- 8.2.2 Time Reversal Symmetry.- 8.3 Radiative Transitions.- 8.4 Crystal Field Theory.- 8.4.1 Crystal Field Splitting of Energy Levels.- 8.4.2 Calculation of Splitting.- 8.5 Independent Components of Material Tensors.- 9. Representations of Space Groups.- 9.1 Representations of Normal Space Groups.- 9.1.1 Decompositions into Cosets.- 9.1.2 Induction of the Representations of R.- 9.2 Allowable Irreducible Representations of the Little Group Gk.- 9.2.1 Projective Representations. Representations with a Factor System for $${\mathcal{G}_{{0k}}} = {\mathcal{G}_k}/\mathbb{T}$$.- 9.2.2 Vector Representations of the Groupe $${\mathcal{J}_k} = {\mathcal{G}_k}/{\mathbb{T}_k}$$.- 9.2.3 Representations of Double Space Groups. Spinor Representations.- 9.3 Projection Operators and Basis Functions.- 9.4 Representations of Magnetic Space Groups.- 9.4.1 Corepresentations of Magnetic Space Groups.- 9.4.2 Time Reversal Symmetry in MII Groups.- 10. Excitation Spectra and Selection Rules in Crystals.- 10.1 Spectra — Some General Statements.- 10.1.1 Bands and Branches.- 10.1.2 Compatibility Relations.- 10.2 Lattice Vibrations.- 10.2.1 Equation of Motion and Symmetry Properties.- 10.2.2 Vibrations of the Diamond Lattice.- 10.3 Electron Energy Bands.- 10.3.1 Symmetrization of Plane Waves.- 10.3.2 Energy Bands and Atomic Levels.- 10.4 Selection Rules for Interactions in Crystals.- 10.4.1 Determination of Reduction Coefficients.- 10.4.2 General Selection Rules.- 10.4.3 Electron-Phonon Interaction.- 10.4.4 Electron-Photon Interaction: Optical Transitions.- 10.4.5 Phonon-Photon Interaction.- 11. Lie Groups and Lie Algebras.- 11.1 General Foundations.- 11.1.1 Infinitesimal Generators and Defining Relations.- 11.1.2 Algebra and Parameter Space.- 11.1.3 Casimir Operators.- 11.2 Unitary Representations of Lie Groups.- 11.3 Clebsch-Gordan Coefficients and the Wigner-Eckart.- Theorem.- 11.4 The Cartan-Weyl Basis for Semisimple Lie Algebras.- 11.4.1 The Lie Group LU (n, ?) and the Lie Algebra An-1..- 11.4.2 The Cartan-Weyl Basis.- 12. Representations by Young Diagrams. The Method of Irreducible Tensors.- 13. Applications of the Theory of Continuous Groups.- 13.1 Elementary Particle Spectra.- 13.1.1 General Remarks.- 13.1.2 Hadronic States.- 13.1.3 Colour States of Quarks.- 13.1.4 A Possible LU (4) Classification.- 13.2 Atomic Spectra.- 13.2.1 Russell-Saunders (LS) Coupling.- 13.2.2 jj Coupling.- 13.3 Nuclear Spectra.- 13.3.1 jj-JI Coupling.- 13.3.2 LSI Coupling.- 13.4 Dynamical Symmetries of Classical Systems.- 14. Internal Symmetries and Gauge Theories.- 14.1 Internal Symmetries of Fields.- 14.2 Gauge Transformations of the First Kind.- 14.2.1 U (1) Gauge Transformations.- 14.2.2 LU (n) Gauge Transformations.- 14.3 Gauge Transformations of the Second Kind.- 14.3.1 U (1) Gauge Transformations of the Second Kind.- 14.3.2 LU (n) Gauge Transformations of the Second Kind.- 14.3.3 A Differential Geometric Discussion of the Yang-Mills Fields.- 14.4 Gauge Theories with Spontaneously Broken Symmetry.- 14.4.1 General Remarks.- 14.4.2 Spontaneous Breaking of a Gauge Symmetry of the First Kind: Goldstone Model.- 14.4.3 Spontaneous Breaking of an Abelian Gauge Symmetry of the Second Kind: Higgs-Kibble Model.- 14.5 Non-Abelian Gauge Theories and Symmetry Breaking.- 14.5.1 The Glashow-Salam-Weinberg Model of the Electro-Weak Interaction.- 14.5.2 Symmetry Breaking in the Glashow-Salam-Weinberg Model.- 14.5.3 Grand Unified Theories: General Remarks.- 14.5.4 LU (5) Group and Georgi-Glashow Model.- 14.5.5 Some Consequences of LU (5) Theory.- Appendices.- A. Character Tables.- B. Representations of Generators.- C. Standard Young-Yamanouchi Representations of the Permutation Groups P3 - P5.- D. Continuous Groups.- E. Stars of k and Symmetry of Special k-Vectors.- F. Noether’s Theorem.- G. Space-Time Symmetry.- G.1 Canonical Transformations and Algebra.- G.2 The Galilei Group and Classical Mechanics.- G.3 Lorentz and Poincaré Groups.- G.4 The Physical Quantities.- H. Goldstone’s Theorem.- I. Remarks on 5-fold Symmetry.- J. Supersymmetry.- K. List of Symbols and Abbreviations.- References.- Additional Reading.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Local Quantum Physics: Fields, Particles,
Book SynopsisThe new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.Trade Review"Indeed, both the expert in the field and the novice will enjoy Haags insightful exposition... This (superb) book is bound to occupy a place on a par with other classics in the mathematical physics literature." Physics Today "...enjoyable reading to anybody interested in the development of fundamental physical theories." Zentralblatt f. MathematikTable of ContentsI. Background.- 1. Quantum Mechanics.- Basic concepts, mathematical structure, physical interpretation..- 2. The Principle of Locality in Classical Physics and the Relativity Theories.- Faraday’s vision. Fields..- 2.1 Special relativity. Poincaré group. Lorentz group. Spinors. Conformal group..- 2.2 Maxwell theory..- 2.3 General relativity..- 3. Poincaré Invariant Quantum Theory.- 3.1 Geometric symmetries in quantum physics. Projective representations and the covering group..- 3.2 Wigner’s analysis of irreducible, unitary representations of the Poincare group. 3.3 Single particle states. Spin..- 3.4 Many particle states: Bose-Fermi alternative, Fock space, creation operators. Separation of CM-motion..- 4. Action Principle.- Lagrangean. Double rôle of physical quantities. Peierls’ direct definition of Poisson brackets. Relation between local conservation laws and symmetries..- 5. Basic Quantum Field Theory.- 5.1 Canonical quantization..- 5.2 Fields and particles..- 5.3 Free fields..- 5.4 The Maxwell-Dirac system. Gauge invariance..- 5.5 Processes..- II. General Quantum Field Theory.- 1. Mathematical Considerations and General Postulates.- 1.1 The representation problem..- 1.2 Wightman axioms..- 2. Hierarchies of Functions.- 2.1 Wightman functions, reconstruction theorem, analyticity in x-space..- 2.2 Truncated functions, clustering. Generating functionals and linked cluster theorem..- 2.3 Time ordered functions..- 2.4 Covariant perturbation theory, Feynman diagrams. Renormalization..- 2.5 Vertex functions and structure analysis..- 2.6 Retarded functions and analyticity in p-space..- 2.7 Schwinger functions and Osterwalder-Schrader theorem..- 3. Physical Interpretation in Terms of Particles.- 3.1 The particle picture: Asymptotic particle configurations and collision theory..- 3.2 Asymptotic fields. S-matrix..- 3.3 LSZ-formalism..- 4. General Collision Theory.- 4.1 Polynomial algebras of fields. Almost local operators..- 4.2 Construction of asymptotic particle states..- 4.3. Coincidence arrangements of detectors..- 4.4 Generalized LSZ-formalism..- 5. Some Consequences of the Postulates.- 5.1 CPT-operator. Spin-statistics theorem. CPT-theorem..- 5.2 Analyticity of the S-matrix..- 5.3 Reeh-Schlieder theorem..- 5.4 Additivity of the energy-momentum-spectrum..- 5.5 Borchers classes..- III. Algebras of Local Observables and Fields.- 1. Review of the Perspective.- Characterization of the theory by a net of local algebras. Bounded operators. Unobservable fields, superselection rules and the net of abstract algebras of observables. Transcription of the basic postulates..- 2. Von Neumann Algebras. C*-Algebras. W*-Algebras.- 2.1 Algebras of bounded operators. Concrete C*-algebras and von Neumann algebras. Isomorphisms. Reduction. Factors. Classification of factors..- 2.2 Abstract algebras and their representations. Abstract C*-algebras. Relation between the C*-norm and the spectrum. Positive linear forms and states. The GNS-construction. Folia of states. Intertwiners. Primary states and cluster property. Purification. W*-algebras..- 3. The Net of Algebras of Local Observables.- 3.1 Smoothness and integration. Local definiteness and local normality..- 3.2 Symmetries and symmetry breaking. Vacuum states. The spectral ideals..- 3.3 Summary of the structure..- 4. The Vacuum Sector.- 4.1 The orthocomplemented lattice of causally complete regions..- 4.2 The net of von Neumann algebras in the vacuum representation..- IV. Charges, Global Gauge Groups and Exchange Symmetry.- 1. Charge Superselection Sectors.- “Strange statistics”. Charges. Selection criteria for relevant sectors. The program and survey of results..- 2. The DHR-Analysis.- 2.1 Localized morphisms..- 2.2 Intertwiners and exchange symmetry (“Statistics”)..- 2.3 Charge conjugation, statistics parameter..- 2.4 Covariant sectors and energy-momentum spectrum..- 2.5 Fields and collision theory..- 3. The Buchholz-Fredenhagen-Analysis.- 3.1 Localized 1-particle states..- 3.2 BF-topological charges..- 3.3 Composition of sectors and exchange symmetry..- 3.4 Charge conjugation and the absence of “infinite statistics”..- 4. Global Gauge Group and Charge Carrying Fields.- Implementation of endomorphisms. Charges with d = 1. Endomorphisms and non Abelian gauge group. DR categories and the embedding theorem..- 5. Low Dimensional Space-Time and Braid Group Statistics.- Statistics operator and braid group representations. The 2+1-dimensional case with BF-charges. Statistics parameter and Jones index..- V. Thermal States and Modular Automorphisms.- 1. Gibbs Ensembles, Thermodynamic Limit, KMS-Condition.- 1.1 Introduction..- 1.2 Equivalence of KMS-condition to Gibbs ensembles for finite volume..- 1.3 The arguments for Gibbs ensembles..- 1.4 The representation induced by a KMS-state..- 1.5 Phases, symmetry breaking and the decomposition of KMS-states..- 1.6 Variational principles and autocorrelation inequalities..- 2. Modular Automorphisms and Modular Conjugation.- 2.1 The Tomita-Takesaki theorem..- 2.2 Vector representatives of states. Convex cones in H..- 2.3 Relative modular operators and Radon-Nikodym derivatives..- 2.4 Classification of factors..- 3. Direct Characterization of Equilibrium States.- 3.1 Introduction..- 3.2 Stability..- 3.3 Passivity..- 3.4 Chemical potential..- 4. Modular Automorphisms of Local Algebras.- 4.1 The Bisognano-Wichmann theorem..- 4.2 Conformal invariance and the theorem of Hislop and Longo..- 5. Phase Space, Nuclearity, Split Property, Local Equilibrium.- 5.1 Introduction..- 5.2 Nuclearity and split property..- 5.3 Open subsystems..- 5.4 Modular nuclearity..- 6. The Universal Type of Local Algebras.- VI. Particles. Completeness of the Particle Picture.- 1. Detectors, Coincidence Arrangements, Cross Sections.- 1.1 Generalities..- 1.2 Asymptotic particle configurations. Buchholz’s strategy..- 2. The Particle Content.- 2.1 Particles and infraparticles..- 2.2 Single particle weights and their decomposition..- 2.3 Remarks on the particle picture and its completeness..- 3. The Physical State Space of Quantum Electrodynamics.- VII. Principles and Lessons of Quantum Physics. A Review of Interpretations, Mathematical Formalism and Perspectives.- 1. The Copenhagen Spirit. Criticisms, Elaborations.- Niels Bohr’s epistemological considerations. Realism. Physical systems and the division problem. Persistent non-classical correlations. Collective coordinates, decoherence and the classical approximation. Measurements. Correspondence and quantization. Time reflection asymmetry of statistical conclusions..- 2. The Mathematical Formalism.- Operational assumptions. “Quantum Logic”. Convex cones..- 3. The Evolutionary Picture.- Events, causal links and their attributes. Irreversibility. The EPR-effect. Ensembles vs. individuals. Decisions. Comparison with standard procedure..- VIII. Retrospective and Outlook.- 1. Algebraic Approach vs. Euclidean Quantum Field Theory.- 2. Supersymmetry.- 3. The Challenge from General Relativity.- 3.1 Introduction..- 3.2 Quantum field theory in curved space-time..- 3.3 Hawking temperature and Hawking radiation..- 3.4 A few remarks on quantum gravity..- Author Index and References.
£66.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Operator Algebras and Quantum Statistical Mechanics: Equilibrium States. Models in Quantum Statistical Mechanics
Book SynopsisFor almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Table of ContentsVolume 2.- States in Quantum Statistical Mechanics.- 5.1. Introduction.- 5.2. Continuous Quantum Systems. I.- 5.3. KMS-States.- 5.4. Stability and Equilibrium.- Models of Quantum Statistical Mechanics.- 6.1. Introduction.- 6.2 Quantum Spin Systems.- 6.3. Continuous Quantum Systems. II.- 6.4. Conclusion.- References.- Books and Monographs.- Articles.- List of Symbols.
£142.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Lectures on Nonlinear Hyperbolic Differential
Book SynopsisIn this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.Table of ContentsPreface.- Contents.- Chap. I: Ordinary differential equations.- Chap. II: Scalar first order equations with one space variable.- Chap. III: Scalar first order equations with several variables.- Chap. IV: First order systems of conservation laws with one space.- Chap. V: Compensated compactness.- Chap. VI: Nonlinear perturbations of the wave equation.- Chap. VII: Nonlinear perturbations of the Klein-Gordon equation.- Chap. VIII: Microlocal analysis.- Chap. IX: Pseudo-differential operators of type 1,1.- Chap. X: Paradifferential calculus.- Chap. XI: Propagation of singularities.- Appendix on pseudo-Riemannian geometry.- References.- Index of notations.- Index.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Foundations of the Classical Theory of Partial Differential Equations
Book SynopsisFrom the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993Trade ReviewFrom the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for the nonspecialists and physicists but in my opinion almost every specialist will find something new for herself/himself in the text. ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993Table of Contents1. Basic Concepts.- 1. Basic Definitions and Examples.- 1.1. The Definition of a Linear Partial Differential Equation.- 1.2. The Role of Partial Differential Equations in the Mathematical Modeling of Physical Processes.- 1.3. Derivation of the Equation for the Longitudinal Elastic Vibrations of a Rod.- 1.4. Derivation of the Equation of Heat Conduction.- 1.5. The Limits of Applicability of Mathematical Models.- 1.6. Initial and Boundary Conditions.- 1.7. Examples of Linear Partial Differential Equations.- 1.8. The Concept of Well-Posedness of a Boundary-value Problem. The Cauchy Problem.- 2. The Cauchy-Kovalevskaya Theorem and Its Generalizations.- 2.1. The Cauchy-Kovalevskaya Theorem.- 2.2. An Example of Nonexistence of an Analytic Solution.- 2.3. Some Generalizations of the Cauchy-Kovalevskaya Theorem. Characteristics.- 2.4. Ovsyannikov’s Theorem.- 2.5. Holmgren’s Theorem.- 3. Classification of Linear Differential Equations. Reduction to Canonical Form and Characteristics.- 3.1. Classification of Second-Order Equations and Their Reduction to Canonical Form at a Point.- 3.2. Characteristics of Second-Order Equations and Reduction to Canonical Form of Second-Order Equations with Two Independent Variables.- 3.3. Ellipticity, Hyperbolicity, and Parabolicity for General Linear Differential Equations and Systems.- 3.4. Characteristics as Solutions of the Hamilton-Jacobi Equation.- 2. The Classical Theory.- 1. Distributions and Equations with Constant Coefficients.- 1.1. The Concept of a Distribution.- 1.2. The Spaces of Test Functions and Distributions.- 1.3. The Topology in the Space of Distributions.- 1.4. The Support of a Distribution. The General Form of Distributions.- 1.5. Differentiation of Distributions.- 1.6. Multiplication of a Distribution by a Smooth Function. Linear Differential Operators in Spaces of Distributions.- 1.7. Change of Variables and Homogeneous Distributions.- 1.8. The Direct or Tensor Product of Distributions.- 1.9. The Convolution of Distributions.- 1.10. The Fourier Transform of Tempered Distributions.- 1.11. The Schwartz Kernel of a Linear Operator.- 1.12. Fundamental Solutions for Operators with Constant Coefficients.- 1.13. A Fundamental Solution for the Cauchy Problem.- 1.14. Fundamental Solutions and Solutions of Inhomogeneous Equations.- 1.15. Duhamel’s Principle for Equations with Constant Coefficients.- 1.16. The Fundamental Solution and the Behavior of Solutions at Infinity.- 1.17. Local Properties of Solutions of Homogeneous Equations with Constant Coefficients. Hypoellipticity and Ellipticity.- 1.18. Liouville’s Theorem for Equations with Constant Coefficients.- 1.19. Isolated Singularities of Solutions of Hypoelliptic Equations.- 2. Elliptic Equations and Boundary-Value Problems.- 2.1. The Definition of Ellipticity. The Laplace and Poisson Equations.- 2.2. A Fundamental Solution for the Laplacian Operator. Green’s Formula.- 2.3. Mean-Value Theorems for Harmonic Functions.- 2.4. The Maximum Principle for Harmonic Functions and the Normal Derivative Lemma.- 2.5. Uniqueness of the Classical Solutions of the Dirichlet and Neumann Problems for Laplace’s Equation.- 2.6. Internal A Priori Estimates for Harmonic Functions. Harnack’s Theorem.- 2.7. The Green’s Function of the Dirichlet Problem for Laplace’s Equation.- 2.8. The Green’s Function and the Solution of the Dirichlet Problem for a Ball and a Half-Space. The Reflection Principle.- 2.9. Harnack’s Inequality and Liouville’s Theorem.- 2.10. The Removable Singularities Theorem.- 2.11. The Kelvin Transform and the Statement of Exterior Boundary-Value Problems for Laplace’s Equation.- 2.12. Potentials.- 2.13. Application of Potentials to the Solution of Boundary-Value Problems.- 2.14. Boundary-Value Problems for Poisson’s Equation in Hölder Spaces. Schauder Estimates.- 2.15. Capacity.- 2.16. The Dirichlet Problem in the Case of Arbitrary Regions (The Method of Balayage). Regularity of a Boundary Point. The Wiener Regularity Criterion.- 2.17. General Second-Order Elliptic Equations. Eigenvalues and Eigenfunctions of Elliptic Operators.- 2.18. Higher-Order Elliptic Equations and General Elliptic Boundary-Value Problems. The Shapiro-Lopatinskij Condition.- 2.19. The Index of an Elliptic Boundary-Value Problem.- 2.20. Ellipticity with a Parameter and Unique Solvability of Elliptic Boundary-Value Problems.- 3. Sobolev Spaces and Generalized Solutions of Boundary-Value Problems.- 3.1. The Fundamental Spaces.- 3.2. Imbedding and Trace Theorems.- 3.3. Generalized Solutions of Elliptic Boundary-Value Problems and Eigenvalue Problems.- 3.4. Generalized Solutions of Parabolic Boundary-Value Problems.- 3.5. Generalized Solutions of Hyperbolic Boundary-Value Problems.- 4. Hyperbolic Equations.- 4.1. Definitions and Examples.- 4.2. Hyperbolicity and Well-Posedness of the Cauchy Problem.- 4.3. Energy Estimates.- 4.4. The Speed of Propagation of Disturbances.- 4.5. Solution of the Cauchy Problem for the Wave Equation.- 4.6. Huyghens’ Principle.- 4.7. The Plane Wave Method.- 4.8. The Solution of the Cauchy Problem in the Plane.- 4.9. Lacunae.- 4.10. The Cauchy Problem for a Strictly Hyperbolic System with Rapidly Oscillating Initial Data.- 4.11. Discontinuous Solutions of Hyperbolic Equations.- 4.12. Symmetric Hyperbolic Operators.- 4.13. The Mixed Boundary-Value Problem.- 4.14. The Method of Separation of Variables.- 5. Parabolic Equations.- 5.1. Definitions and Examples.- 5.2. The Maximum Principle and Its Consequences.- 5.3. Integral Estimates.- 5.4. Estimates in Hölder Spaces.- 5.5. The Regularity of Solutions of a Second-Order Parabolic Equation.- 5.6. Poisson’s Formula.- 5.7. A Fundamental Solution of the Cauchy Problem for a Second-Order Equation with Variable Coefficients.- 5.8. Shilov-Parabolic Systems.- 5.9. Systems with Variable Coefficients.- 5.10. The Mixed Boundary-Value Problem.- 5.11. Stabilization of the Solutions of the Mixed Boundary-Value Problem and the Cauchy Problem.- 6. General Evolution Equations.- 6.1. The Cauchy Problem. The Hadamard and Petrovskij Conditions.- 6.2. Application of the Laplace Transform.- 6.3. Application of the Theory of Semigroups.- 6.4. Some Examples.- 7. Exterior Boundary-Value Problems and Scattering Theory.- 7.1. Radiation Conditions.- 7.2. The Principle of Limiting Absorption and Limiting Amplitude.- 7.3. Radiation Conditions and the Principle of Limiting Absorption for Higher-Order Equations and Systems.- 7.4. Decay of the Local Energy.- 7.5. Scattering of Plane Waves.- 7.6. Spectral Analysis.- 7.7. The Scattering Operator and the Scattering Matrix.- 8. Spectral Theory of One-Dimensional Differential Operators.- 8.1. Outline of the Method of Separation of Variables.- 8.2. Regular Self-Adjoint Problems.- 8.3. Periodic and Antiperiodic Boundary Conditions.- 8.4. Asymptotics of the Eigenvalues and Eigenfunctions in the Regular Case.- 8.5. The Schrödinger Operator on a Half-Line.- 8.6. Essential Self-Adjointness and Self-Adjoint Extensions. The Weyl Circle and the Weyl Point.- 8.7. The Case of an Increasing Potential.- 8.8. The Case of a Rapidly Decaying Potential.- 8.9. The Schrödinger Operator on the Entire Line.- 8.10. The Hill Operator.- 9. Special Functions.- 9.1. Spherical Functions.- 9.2. The Legendre Polynomials.- 9.3. Cylindrical Functions.- 9.4. Properties of the Cylindrical Functions.- 9.5. Airy’s Equation.- 9.6. Some Other Classes of Functions.- References.- Author Index.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Scaling Limits of Interacting Particle Systems
Book SynopsisThis book has been long awaited in the "interacting particle systems" community. Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator. It presents the techniques used in the proof of the hydrodynamic behavior of interacting particle systems.Trade Review"Das Buch ist nach Meinung des Rezensenten eine gelungene Einführung in ein interessantes Gebiet der modernen Stochastik und mathematischen Physik und stellt einen fest umrissenen Gegenstand umfassend dar, vor allem den analytisch-methodischen Aspekt. ... Die Beweise sind übersichtlich und gut gegliedert, was das Nachvollziehen der Argumente sehr erleichtert; die didaktische Leistung der Autoren in diesem Punkt ist beeindruckend. Ein sorgfältig zusammengestelltes Literaturverzeichnis von etwa 400 Titeln schließt das Buch ab. Ingesamt ein sehr gut geschriebener und nützlicher Band."DMV Jahresbericht, 103. Band, Heft 3, November 2001Table of Contents1. An Introductory Example: Independent Random Walks.- 2. Some Interacting Particle Systems.- 3. Weak Formulations of Local Equilibrium.- 4. Hydrodynamic Equation of Symmetric Simple Exclusion Processes.- 5. An Example of Reversible Gradient System: Symmetric Zero Range Processes.- 6. The Relative Entropy Method.- 7. Hydrodynamic Limit of Reversible Nongradient Systems.- 8. Hydrodynamic Limit of Asymmetric Attractive Processes.- 9. Conservation of Local Equilibrium for Attractive Systems.- 10. Large Deviations from the Hydrodynamic Limit.- 11. Equilibrium Fluctuations of Reversible Dynamics.- Appendices.- 1. Markov Chains on a Countable Space.- 1.1 Discrete Time Markov Chains.- 1.2 Continuous Time Markov Chains.- 1.3 Kolmogorov’s Equations, Generators.- 1.4 Invariant Measures, Reversibility and Adjoint Processes.- 1.5 Some Martingales in the Context of Markov Processes.- 1.6 Estimates on the Variance of Additive Functionals of Markov Processes.- 1.7 The Feynman-Kac Formula.- 1.8 Relative Entropy.- 1.9 Entropy and Markov Processes.- 1.10 Dirichlet Form.- 1.11 A Maximal Inequality for Reversible Markov Processes.- 2. The Equivalence of Ensembles, Large Deviation Tools and Weak Solutions of Quasi-Linear Differential Equations.- 2.1 Local Central Limit Theorem and Equivalence of Ensembles.- 2.2 On the Local Central Limit Theorem.- 2.3 Remarks on Large Deviations.- 2.4 Weak Solutions of Nonlinear Parabolic Equations.- 2.5 Entropy Solutions of Quasi-Linear Hyperbolic Equations.- 3. Nongradient Tools: Spectral Gap and Closed Forms.- 3.1 On the Spectrum of Reversible Markov Processes.- 3.2 Spectral Gap for Generalized Exclusion Processes.- 3.4 Closed and Exact Forms.- 3.5 Comments and References.- References.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Field Theory in Condensed Matter Physics
Book SynopsisThis is an approachable introduction to the important topics and recent developments in the field of condensed matter physics. First, the general language of quantum field theory is developed in a way appropriate for dealing with systems having a large number of degrees of freedom. This paves the way for a description of the basic processes in such systems. Applications include various aspects of superfluidity and superconductivity, as well as a detailed description of the fractional quantum Hall liquid.Table of ContentsQuantum Mechanics and Fundamentals of Quantum Field Theory.- Path Integral Quantization.- Broken Symmetry and Phase Transition.- Some Applications - Warming Ups.- Superconductivity.- Quantum Hall Liquids and Chern--Simons Gauge Field.- Appendix.
£132.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Hamiltonian Methods in the Theory of Solitons
Book SynopsisThe main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.Trade Review Table of ContentsThe Nonlinear Schrödinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples and Their General Properties.- Fundamental Continuous Models.- Fundamental Models on the Lattice.- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models.- Conclusion.- Conclusion.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Vector Calculus
Book SynopsisVector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.Trade ReviewP.C. Matthews Vector Calculus "Written for undergraduate students in mathematics, the book covers the material in a comprehensive but concise manner, combining mathematical rigor with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which essential for a full understanding of the subject." — ZENTRALBLATT MATH Table of Contents1. Vector Algebra.- 1.1 Vectors and scalars.- 1.1.1 Definition of a vector and a scalar.- 1.1.2 Addition of vectors.- 1.1.3 Components of a vector.- 1.2 Dot product.- 1.2.1 Applications of the dot product.- 1.3 Cross product.- 1.3.1 Applications of the cross product.- 1.4 Scalar triple product.- 1.5 Vector triple product.- 1.6 Scalar fields and vector fields.- 2. Line, Surface and Volume Integrals.- 2.1 Applications and methods of integration.- 2.1.1 Examples of the use of integration.- 2.1.2 Integration by substitution.- 2.1.3 Integration by parts.- 2.2 Line integrals.- 2.2.1 Introductory example: work done against a force.- 2.2.2 Evaluation of line integrals.- 2.2.3 Conservative vector fields.- 2.2.4 Other forms of line integrals.- 2.3 Surface integrals.- 2.3.1 Introductory example: flow through a pipe.- 2.3.2 Evaluation of surface integrals.- 2.3.3 Other forms of surface integrals.- 2.4 Volume integrals.- 2.4.1 Introductory example: mass of an object with variable density.- 2.4.2 Evaluation of volume integrals.- 3. Gradient, Divergence and Curl.- 3.1 Partial differentiation and Taylor series.- 3.1.1 Partial differentiation.- 3.1.2 Taylor series in more than one variable.- 3.2 Gradient of a scalar field.- 3.2.1 Gradients, conservative fields and potentials.- 3.2.2 Physical applications of the gradient.- 3.3 Divergence of a vector field.- 3.3.1 Physical interpretation of divergence.- 3.3.2 Laplacian of a scalar field.- 3.4 Curl of a vector field.- 3.4.1 Physical interpretation of curl.- 3.4.2 Relation between curl and rotation.- 3.4.3 Curl and conservative vector fields.- 4. Suffix Notation and its Applications.- 4.1 Introduction to suffix notation.- 4.2 The Kronecker delta ?ij.- 4.3 The alternating tensor ?ijk.- 4.4 Relation between ?ijk and ?ij.- 4.5 Grad, div and curl in suffix notation.- 4.6 Combinations of grad, div and curl.- 4.7 Grad, div and curl applied to products of functions.- 5. Integral Theorems.- 5.1 Divergence theorem.- 5.1.1 Conservation of mass for a fluid.- 5.1.2 Applications of the divergence theorem.- 5.1.3 Related theorems linking surface and volume integrals.- 5.2 Stokes’s theorem.- 5.2.1 Applications of Stokes’s theorem.- 5.2.2 Related theorems linking line and surface integrals.- 6. Curvilinear Coordinates.- 6.1 Orthogonal curvilinear coordinates.- 6.2 Grad, div and curl in orthogonal curvilinear coordinate systems.- 6.2.1 Gradient.- 6.2.2 Divergence.- 6.2.3 Curl.- 6.3 Cylindrical polar coordinates.- 6.4 Spherical polar coordinates.- 7. Cartesian Tensors.- 7.1 Coordinate transformations.- 7.2 Vectors and scalars.- 7.3 Tensors.- 7.3.1 The quotient rule.- 7.3.2 Symmetric and anti-symmetric tensors.- 7.3.3 Isotropic tensors.- 7.4 Physical examples of tensors.- 7.4.1 Ohm’s law.- 7.4.2 The inertia tensor.- 8. Applications of Vector Calculus.- 8.1 Heat transfer.- 8.2 Electromagnetism.- 8.2.1 Electrostatics.- 8.2.2 Electromagnetic waves in a vacuum.- 8.3 Continuum mechanics and the stress tensor.- 8.4 Solid mechanics.- 8.5 Fluid mechanics.- 8.5.1 Equation of motion for a fluid.- 8.5.2 The vorticity equation.- 8.5.3 Bernoulli’s equation.- Solutions.
£29.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Wissenschaftliches Rechnen
Book SynopsisDas Ziel des nun auch in deutscher Übersetzung erhältlichen Buches ist es, angewandte Mathematik und Ingenieurmathematik so darzustellen, wie sie heutzutage Anwendung findet. Das Buch basiert auf dem Kurs „Wissenschaftliches Rechnen" des Massachusetts Institute of Technology und versucht, Konzepte und Algorithmen zusammenzuführen. Beginnend mit der angewandten linearen Algebra entwickeln die Autoren die Methoden der finiten Differenzen und finiten Elemente – stets in Verbindung mit Anwendungen in zahlreichen Wissensgebieten.Trade Review“... Der in jeder Hinsicht hervorragende Text von Strang wird für lange Zeit eine Standardreferenz in der Literatur zur Ausbildung im wissenschaftlichen Rechnen sein. Es gibt viele gute Gründe, ihn zu besitzen ...” (H.R. Schneebeli, in: Elemente der Mathematik, jg. 67, S. 200 f. 2012)“... Das Buch enthält zahlreiche Aufgaben in unterschiedlichen Schwierigkeitsgraden und drei Anhänge und ist, wenn man es nicht als Begleitbuch zu einer Vorlesung gebraucht, hervorragend zum Stöbern geeignet. ... ist das Buch äußerst empfehlenswert nicht nur für Ingenieure. Teile des Buches sind sicher auch schon für begabte und interessierte Schülerinnen und Schüler geeignet und von Pseudoanwendungen in Schulbüchern genervte Lehrkräfte an unseren Gymnasien können hier realistische Anwendungen finden, die man mit Mathematik bearbeiten kann.“ (in: Mathematische Semesterberichte, 2012, Issue 1)“... in diesem umfangreichen, ursprünglich in englisch erschienenem Werk mit mathematischer Exaktheit und anwendungsorientierter Zielrichtung ... Angesprochen sind vorwiegend Studierende der Mathematik und der Ingenieurwissenschaften. ... Der kurze Anhang ist allenfalls geeignet, Erinnerungslücken zu schließen.“ (Wolfgang Grölz, in: ekz-Informationsdienst, 2010, Vol. 2010/34)Table of ContentsAngewandte lineare Algebra.- Ein Grundmuster der angewandten Mathematik.- Randwertprobleme.- Fourier-Reihen und Fourier-Integrale.- Analytische Funktionen.- Anfangswertprobleme.- Große Systeme.- Optimierung und Minimumprinzip.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Number Theory in Science and Communication: With
Book Synopsis"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin GardnerTrade ReviewFrom the reviews of the fifth edition:“Number theory has been a very active field in the last twenty-seven years, and Schroeder’s text has a palimpsest quality, with later mathematical advances layered on earlier ones. … Number Theory in Science and Communication is rewarding to browse, or as a jumping-off point for further research … . It would be a good source of student projects in an undergraduate discrete mathematics or number theory course.” (Ursula Whitcher, The Mathematical Association of America, March, 2011)Table of ContentsA Few Fundamentals.- The Natural Numbers.- Primes.- The Prime Distribution.- Some Simple Applications.- Fractions: Continued, Egyptian and Farey.- Congruences and the Like.- Linear Congruences.- Diophantine Equations.- The Theorems of Fermat Wilson and Euler.- Permutations Cycles and Derangements.- Cryptography and Divisors.- Euler Trap Doors and Public-Key Encryption.- The Divisor Functions.- The Prime Divisor Functions.- Certified Signatures.- Primitive Roots.- Knapsack Encryption.- Residues and Diffraction.- Quadratic Residues.- Chinese and Other Fast Algorithms.- The Chinese Remainder Theorem and Simultaneous Congruences.- Fast Transformation and Kronecker Products.- Quadratic Congruences.- Pseudoprimes, Möbius Transform, and Partitions.- Pseudoprimes Poker and Remote Coin Tossing.- The Möbius Function and the Möbius Transform.- Generating Functions and Partitions.- From Error Correcting Codes to Covering Sets.- Cyclotomy and Polynomials.- Cyclotomic Polynomials.- Linear Systems and Polynomials.- Polynomial Theory.- Galois Fields and More Applications.- Galois Fields.- Spectral Properties of Galois Sequences.- Random Number Generators.- Waveforms and Radiation Patterns.- Number Theory Randomness and “Art”.- Self-Similarity, Fractals and Art.- Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter.
£56.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Group Theory: Application to the Physics of Condensed Matter
Book SynopsisThis concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.Trade ReviewFrom the reviews:"It was developed for a graduate course taught mostly by Millie Dresselhaus at MIT for more than 30 years, with many revisions of lecture notes. Very much a graduate text or specialist monograph, the book covers a wealth of applications across solid-state physics. … The book can be warmly recommended to students and researchers in solid-state physics, either to serve as a text for an advanced lecture course or for individual study … ." (Volker Heine, Physics Today, November, 2008)"This textbook is based on the authors’ pedagogical experience during their 30 years at MIT. … the book develops all of the relevant mathematics (linear algebra) and the necessary physics (quantum mechanics), it is eminently suitable to a wide audience in physics, chemistry and materials science." (Barry R. Masters, Optics and Photonics News, July/August, 2009)“This is an excellent text … . originates from lectures by Charles Kittel and J. H. van Vleck in the 1950s and much of the material was presented in courses by the authors over the last three decades. The material is meant for Electrical Engineering and Physics students at the graduate level … . has exercises at the end of each chapter and an extensive set of appendices. The exposition is clear and detailed. This is a very good book for its target audience.” (W. Miller Jr., Zentralblatt MATH, Vol. 1175, 2010)“The goal of the book under review is to teach group theory in close connection to applications. … Every chapter of the book finishes with several selected problems. Specific to this book is the feature that every abstract theoretical group concept is introduced and applied in a concrete physical way. This is why the book is very useful for anyone interested in applications of group theory to the wide range of condensed matter phenomena.” (Oktay K. Pashaev, Mathematical Reviews, Issue 2010 i)“It is highly welcomed because of its well-thought structuring and the plenty of non-trivial examples. The authors develop those parts of the theory of groups which are interesting for physicists, from chapter to chapter offering nearly at any step one or more informative application.” (G. Kowol, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)Table of ContentsBasic Mathematics.- Basic Mathematical Background: Introduction.- Representation Theory and Basic Theorems.- Character of a Representation.- Basis Functions.- Introductory Application to Quantum Systems.- Splitting of Atomic Orbitals in a Crystal Potential.- Application to Selection Rules and Direct Products.- Molecular Systems.- Electronic States of Molecules and Directed Valence.- Molecular Vibrations, Infrared, and Raman Activity.- Application to Periodic Lattices.- Space Groups in Real Space.- Space Groups in Reciprocal Space and Representations.- Electron and Phonon Dispersion Relation.- Applications to Lattice Vibrations.- Electronic Energy Levels in a Cubic Crystals.- Energy Band Models Based on Symmetry.- Spin–Orbit Interaction in Solids and Double Groups.- Application of Double Groups to Energy Bands with Spin.- Other Symmetries.- Time Reversal Symmetry.- Permutation Groups and Many-Electron States.- Symmetry Properties of Tensors.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Synergetics: Introduction and Advanced Topics
Book SynopsisThis book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.Table of ContentsAn Introduction.- Advanced Topics.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Mechanics: Symbolism of Atomic Measurements
Book SynopsisA unique legacy, these lecture notes of Schwinger’s course held at the University of California at Los Angeles were carefully edited by his former collaborator Berthold-Georg Englert and constitute both a self-contained textbook on quantum mechanics and an indispensable source of reference on this fundamental subject by one of the foremost thinkers of twentieth century physics.Trade ReviewFrom the reviews: "Quantum Mechanics: Symbolism of Atomic Measurements is not just another textbook on quantum mechanics. Rather, it contains truly novel elements of both content and style. In particular, Schwinger begins his treatment not with de Broglie waves or the Schrödinger equation but rather with the measurement process. His idea is to derive, or at least make plausible, the formalism of state vectors, bras and kets, by reference to quantum measurements such as the Stern-Gerlach experiment. This [...] is simply the basis of a new way of teaching quantum mechanics. This opening chapter should be of interest to all scholars of quantum theory and might form a new topic of research for philosophers of quantum mechanics." (Contemporary Physics, 44/2, 2003) "There are dozen of excellent textbooks on the market. But this one really is different." (T. Kibble, The Times Higher Education Supplement, 2001) "The material covered is superficially similar to that of a typical graduate quantum mechanics course [...] However, each chapter has beautiful and unusual treatments of familiar topics. [...] This book would make an outstanding supplement and reference for a graduate quantum mechanics course. Theoretical physicists will delight in this wonderful book, which should be available in the library system of any institution with a research or graduate program in physics. Graduate students through professionals." (CHOICE, Dec. 2001) "The book is a tour-de-force. Once the groundwork is laid, he goes into subjects with the mathematical virtuosity for which he was famous – not advanced mathematics, but the incredible use of simple mathematics. … there are gems throughout the book. … it is a wonderful book for a professor to own, like Feyman’s lectures, because there is so much to learn from it. … The book was lovingly edited from some UCLA lecture notes, by Berthold-Georg Englert, a longtime student and assistant of Schwinger’s … ." (Daniel Greenberger, American Journal of Physics, Vol 71 (9), 2003) "Editor Englert has performed a service for physicists everywhere by making available this book, which is based on Schwinger’s unpublished UCLA lecture notes. … each chapter has beautiful and unusual treatments of familiar topics. … There are excellent problems at the end of each chapter. This book would make an outstanding supplement and reference for a graduate quantum mechanics course. Theoretical physicists will delight in this wonderful book, which should be available in the library system of any institution with a research or graduate program … ." (M. C. Ogilvie, CHOICE, December, 2001) "The book commences with an absorbing prologue in which Schwinger talks us through the development of quantum mechanic and quantum field theory in an easy conversational style. … The book is packed with exercises for the reader to attempt. … Anyone who works religiously through these exercises will acquire a thoroughly adequate command of quantum mechanics." (W. Cox, Mathematical Reviews, Issue 2002 h) "Quantum mechanics: Symbolism of Atomic Measurements is not just another textbook on quantum mechanics. Rather, it contains truly novel elements of both content and style. … This opening chapter should be of interest to all scholars of quantum theory and might form a new topic of research for philosophers of quantum mechanics. Throughout the text, new material is presented at a breathless pace. All the usual elements of the subject are there, but Schwinger’s presentation reveals surprises in even the most familiar of these." (S. M. Barnett, Contemporary Physics, Vol. 44 (2), 2003) "In the beginning, the editor has added an important material in the form of a prologue … . This is one of the best treatments of the philosophy of quantum mechanics, which I have come across. … One of the major features of the book is the incorporation of a large number of problems … . the contents of the problems are well integrated in the text and have become part of it. This has caused a rich and tight structure of the logical arguments." (S. S. Bhattacharyya, Indian Journal of Physics, Vol. 76B (3), 2002) "This unique textbook is based upon the lecture notes that Julian Schwinger wrote up for the students of the quantum mechanics course … . this book would probably make an ideal quantum mechanics reference … . There are a large number of problems included at the end of each chapter, which comprise an excellent resource for any lecturer … . this textbook is a unique resource, which provides an insight into the thoughts and deliberations of one of this century’s giants of quantum mechanics." (P. C. Dastoor, The Physicist, Vol. 38 (5), 2001) "There are dozens of excellent textbooks on the market. But this one really is different. … there is a carefully argued historical and philosophical prologue that sets the scene, centred on the two key features of quantum physics – atomicity and its probabilistic character; this alone would make the book worthwhile. The emphasis on discrete variables is a very modern approach… . To a theoretical physicist, this book is a delight and a wonderful resource. … This is a book I shall treasure." (Tom Kibble, Times Higher Education Supplement, September, 2001)Table of ContentsPrologue.- A. Fall Quarter: Quantum Kinematics.- 1 Measurement Algebra.- 2 Continuous q, p Degree of Freedom.- 3 Angular Momentum.- 4 Galilean Invariance.- B. Winter Quarter: Quantum Dynamics.- 5 Quantum Action Principle.- 6 Elementary Applications.- 7 Harmonic Oscillators.- 8 Hydrogenic Atoms.- C. Spring Quarter: Interacting Particles.- 9 Two-Particle Coulomb Problem.- 10 Identical Particles.- 11 Many-Electron Atoms.- 12 Electromagnetic Radiation.
£52.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Statistical Physics: An Advanced Approach with
Book SynopsisThe book is divided into two parts. The first part looks at the modeling of statistical systems before moving on to an analysis of these systems. This second edition contains new material on: estimators based on a probability distribution for the parameters; identification of stochastic models from observations; and statistical tests and classification methods.Table of Contents1 Statistical Physics: Is More than Statistical Mechanics.- I Modeling of Statistical Systems.- 2 Random Variables: Fundamentals of Probability Theory and Statistics.- 3 Random Variables in State Space: Classical Statistical Mechanics of Fluids.- 4 Random Fields: Textures and Classical Statistical Mechanics of Spin Systems.- 5 Time-Dependent Random Variables: Classical Stochastic Processes.- 6 Quantum Random Systems.- 7 Changes of External Conditions.- II Analysis of Statistical Systems.- 8 Estimation of Parameters.- 9 Signal Analysis: Estimation of Spectra.- 10 Estimators Based on a Probability Distribution for the Parameters.- 11 Identification of Stochastic Models from Observations.- 12 Estimating the Parameters of a Hidden Stochastic Model.- 13 Statistical Tests and Classification Methods.- Appendix: Random Number Generation for Simulating Realizations of Random Variables.- Problems.- Hints and Solutions.- References.
£66.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Percolation
Book SynopsisPercolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.Table of Contents1 What is Percolation?.- 2 Some Basic Techniques.- 3 Critical Probabilities.- 4 The Number of Open Clusters per Vertex.- 5 Exponential Decay.- 6 The Subcritical Phase.- 7 Dynamic and Static Renormalization.- 8 The Supercritical Phase.- 9 Near the Critical Point: Scaling Theory.- 10 Near the Critical Point: Rigorous Results.- 11 Bond Percolation in Two Dimensions.- 12 Extensions of Percolation.- 13 Percolative Systems.- Appendix I. The Infinite-Volume Limit for Percolation.- Appendix II. The Subadditive Inequality.- List of Notation.- References.- Index of Names.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Field Theory in Condensed Matter Physics
Book SynopsisThis is an approachable introduction to the important topics and recent developments in the field of condensed matter physics. First, the general language of quantum field theory is developed in a way appropriate for dealing with systems having a large number of degrees of freedom. This paves the way for a description of the basic processes in such systems. Applications include various aspects of superfluidity and superconductivity, as well as a detailed description of the fractional quantum Hall liquid.Table of ContentsQuantum Mechanics and Fundamentals of Quantum Field Theory.- Path Integral Quantization.- Broken Symmetry and Phase Transition.- Some Applications - Warming Ups.- Superconductivity.- Quantum Hall Liquids and Chern--Simons Gauge Field.- Appendix.
£132.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Heat Kernel and Quantum Gravity
Book SynopsisThis book is aimed at theoretical as well as primarily physicists graduate students in field working quantum theory, quantum gravity, theories, gauge to sdme and and, it is not extent, general relativity cosmology. Although aimed at a I that it also be of level, hope in mathematically rigorous may terest to mathematical and mathematicians in physicists working spectral of differential mani geometry, spectral asymptotics on operators, analysis differential and mathematical methods in folds, geometry quantum theory. Thisbook will be considered too abstract some but certainly by physicists, not detailed and most mathematicians. This in completeenoughby means, thatthe material is at the level of particular, presented "physical" So, rigor. there theorems and areno and technicalcalculationsare lemmas, proofs long omitted. I tried detailed to a ofthe basic Instead, give presentation ideas, methodsandresults. Itried makethe to as andcom Also, exposition explicit as the lessabstractandhaveillustratedthe plete possible, methods language and results withsome As is well "onecannot examples. known, cover every in an text. The in this thing", especially introductory approach presented book the lines is a further of the so called along goes (and development) fieldmethod ofDe Witt. As a Ihavenot dealt at background consequence, allwithmanifoldswith boundary,non Laplacetype (ornonminimal) opera Riemann Cartan manifolds well with as as recent tors, developments many and advanced such Ashtekar's more as topics, approach,supergravity,strings, matrix etc. The membranes, interested reader is referred models, M theory tothe literature.Trade Review"This monograph rightly belongs to a series ‘Lecture notes in Physics’, as it represents a well-written review of main results by the author, who is a recognized expert on heat kernel techniques in quantum gravity. [...] The results exposed in this book reflect the major contributions of the author to differential geometry and the theory of differential operators. They have many applications in quantum field theory with background fields, and indeed, the book can be used as a text for a short graduate course in the heat kernel techniques and their quantum gravity." (Mathematical Reviews 2003a)Table of ContentsBackground Field Method in Quantum Field Theory.- Technique for Calculation of De Witt Coefficients.- Partial Summation of Schwinger-De Witt Expansion.- Higher-Derivative Quantum Gravity.- Conclusion.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Geometry of Minkowski Space-Time
Book SynopsisThis book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry.The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions.The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time.Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.Table of ContentsIntroduction.- Hyperbolic Numbers.- Geometrical Representation of Hyperbolic Numbers.- Trigonometry in the Hyperbolic (Minkowski) Plane.- Equilateral Hyperbolas and Triangles in the Hyperbolic Plane.- The Motions in Minkowski Space-Time (Twin Paradox).- Some Final Considerations.
£47.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Field Theory III: Gauge Theory: A Bridge between Mathematicians and Physicists
Book SynopsisIn this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a ParadigmPart II: Ariadne's Thread in Gauge TheoryPart III: Einstein's Theory of Special RelativityPart IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). Trade ReviewFrom the reviews:“This book is the third volume of a complete exposition of the important mathematical methods used in modern quantum field theory. It presents the very basic formalism, important results, and the most recent advances emphasizing the applications to gauge theory. … the book’s greatest strength is Zeidler’s zeal to help students understand fundamental mathematics better. I thus find the book extremely useful since it signifies the role of mathematics for the road to reality … .” (Gert Roepstorff, Zentralblatt MATH, Vol. 1228, 2012)“The present book is a good companion to the literature on the subject of the volume title, especially for those already familiar with it. … the book touches upon a large number of subjects on the interface between mathematics and physics, providing a good overview of gauge theory in both fields. It contains lots of background material, many historical remarks, and an extensive bibliography that helps the interested reader to continue his or her more thorough studies elsewhere.” (Walter D. van Suijlekom, Mathematical Reviews, Issue 2012 m)Table of ContentsPrologue.- Part I. The Euclidean Manifold as a Paradigm: 1. The Euclidean Space E3 (Hilbert Space and Lie Algebra Structure).- 2. Algebras and Duality (Tensor Algebra, Grassmann Algebra, Cli_ord Algebra, Lie Algebra).- 3. Representations of Symmetries in Mathematics and Physics.- 4. The Euclidean Manifold E3.- 5. The Lie Group U(1) as a Paradigm in Harmonic Analysis and Geometry.- 6. Infinitesimal Rotations and Constraints in Physics.- 7. Rotations, Quaternions, the Universal Covering Group, and the Electron Spin.- 8. Changing Observers - A Glance at Invariant Theory Based on the Principle of the Correct Index Picture.- 9. Applications of Invariant Theory to the Rotation Group.- 10. Temperature Fields on the Euclidean Manifold E3.- 11. Velocity Vector Fields on the Euclidean Manifold E3.- 12. Covector Fields and Cartan's Exterior Differential - the Beauty of Differential Forms.- Part II. Ariadne's Thread in Gauge Theory: 13. The Commutative Weyl U(1)-Gauge Theory and the Electromagnetic Field.- 14. Symmetry Breaking.- 15. The Noncommutative Yang{Mills SU(N)-Gauge Theory.- 16. Cocycles and Observers.- 17. The Axiomatic Geometric Approach to Bundles.- Part III. Einstein's Theory of Special Relativity: 18. Inertial Systems and Einstein's Principle of Special Relativity.- 19. The Relativistic Invariance of the Maxwell Equations.- 20. The Relativistic Invariance of the Dirac Equation and the Electron Spin.- Part IV. Ariadne's Thread in Cohomology: 21. The Language of Exact Sequences.- 22. Electrical Circuits as a Paradigm in Homology and Cohomology.- 23. The Electromagnetic Field and the de Rham Cohomology.- Appendix.- Epilogue.- References.- List of Symbols.- Index
£189.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG 3+1 Formalism in General Relativity: Bases of
Book SynopsisThis graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.Trade ReviewFrom the reviews:“The monograph originating from lectures is devoted to the 3+1 formalism in general relativity. It starts with three chapters on basic differential geometry, the geometry of single hypersurfaces embedded in space-time, and the foliation of space-time by a family of spacelike hypersurfaces. … With the attempt to make the text self-consistent and complete, the calculations are … detailed such that the book is well suitable for undergraduate and graduate students.” (Horst-Heino von Borzeszkowski, Zentralblatt MATH, Vol. 1254, 2013)“This book is written for advanced students and researchers who wish to learn the mathematical foundations of various approaches that have been proposed to solve initial value problems (with constraints) for the Einstein equations numerically. … Even for experts it may be useful, as it includes an extensive bibliography up to 2011.” (Hans-Peter Künzle, Mathematical Reviews, January, 2013)Table of ContentsBasic Differential Geometry.- Geometry of Hypersurfaces.- Geometry of Foliations.- 3+1 decomposition of Einstein Equation.- 3+1 Equations for Matter and Electromagnetic Field.- Conformal Decompositon.- Asymptotic Flatness and Global Quantities.- The Initial Data Problem.- Choice of Foliation and Spatial Coordiinates.- Evolution Schemes.- Conformal Killing Operator and Conformal Vector Laplacian.- Sage Codes.
£47.49
Springer Fachmedien Wiesbaden Grundkurs Theoretische Physik 6: Statistische
Book SynopsisDer Grundkurs Theoretische Physik deckt in 7 Bänden alle für das Diplom und für Bachelor/Master-Studiengänge maßgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester notwendige theoretisch-physikalische Rüstzeug. Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffs. Der 6. Band zur Statistischen Physik wurde für die Neuauflage grundlegend überarbeitet und um aktuelle Entwicklungen ergänzt. Durch die zweifarbige Gestaltung ist der Stoff jetzt noch übersichtlicher gegliedert.Table of ContentsKlassische statistische Physik.- Quantenstatistik.- Quantengase.- Phasenübergänge.- Lösungen der Übungsaufgaben.
£47.49
Springer Fachmedien Wiesbaden Grundkurs Theoretische Physik 5/1:
Book SynopsisDer Grundkurs Theoretische Physik deckt in 7 Bänden die im Diplom- und Bachelor/Master-Studium maßgeblichen Gebiete ab und vermittelt das im jeweiligen Semester benötigte theoretisch-physikalische Rüstzeug. Der erste Teil von Band 5 beginnt mit einer Begründung der Quantenmechanik und der Zusammenstellung ihrer formalen Grundlagen, um dann Konzepte und Begriffsbildungen an Modellsystemen zu illustrieren. Der Band enthält Übungsaufgaben und Kontrollfragen zur Vertiefung des Stoffs. Die überarbeitete und ergänzte Neuauflage ist zweifarbig gestaltet.Table of ContentsInduktive Begründung der Wellenmechanik.- Schrödinger-Gleichung.- Grundlagen der Quantenmechanik (Dirac-Formalismus).- Einfache Modellsysteme.- Lösungen der Übungsaufgaben.
£36.09
Springer Fachmedien Wiesbaden Praktische Mathematik mit MATLAB, Scilab und
Book SynopsisDer Band bietet eine Schritt-für-Schritt-Einführung in das numerische Rechnen mit den Programmen MATLAB, Scilab und Octave. Anhand zahlreicher Beispiele zeigen die Autoren, wie die mathematischen Tools zur Lösung mathematischer, physikalischer und insbesondere ingenieurwissenschaftlicher Aufgaben eingesetzt werden können. Dazu gehören die Lösung von linearen Gleichungssystemen, nichtlinearen Gleichungen und Differentialgleichungen, die Fourier- und Wavelet-Transformation, Kurvenanpassung und Interpolation sowie die numerische Integration.Trade Review“... Zum Nachschlagen enthält jedes Kapitel eine Zusammenfassung, und ganz am Ende stehen einige Testfragen sowie eine kleine Literaturliste, so dass sich der neugierige Leser weiteres Futter verschaffen kann. ... erkunden die Autoren einige Teilbereiche der numerischen Mathematik, die für Anfänger geeignet sind. ... Die vielen Beispiele und Aufgaben unterstützen den Leser enorm ... Wer sich für das Lösen numerischer Probleme mit zeitgemäßen Werkzeugen interessiert, der kann zunächst bedenkenlos zu diesem Werk greifen.” (Harald Löwe, in: Mathematische Semesterberichte, Jg. 62, 2015, S. 114 f.) Table of Contents
£37.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Chromodynamics on the Lattice: An Introductory Presentation
Book SynopsisQuantum chromodynamics (QCD) is the fundamental quantum ?eld theory of quarks and gluons. In order to discuss it in a mathematically well-de?ned way, the theory has to be regularized. Replacing space-time by a Euclidean lattice has proven to be an e?cient approach which allows for both theor- ical understanding and computational analysis. Lattice QCD has become a standard tool in elementary particle physics. Asthetitlealreadysays:thisbookisintroductory!Thetextisintendedfor newcomerstothe?eld,servingasastartingpoint.Wesimplywantedtohavea bookwhichwecanputintothehandsofanadvancedstudentfora?rstreading on lattice QCD. This imaginary student brings as a prerequisite knowledge of higher quantum mechanics, some continuum quantum ?eld theory, and basic facts of elementary particle physics phenomenology. In view of the wealth of applications in current research the topics p- sented here are limited and we had to make some painful choices. We discuss QCD but omit most other lattice ?eld theory applications like scalar th- ries, gauge-Higgs models, or electroweak theory. Although we try to lead the reader up to present day understanding, we cannot possibly address all on- ing activities, in particular concerning the role of QCD in electroweak theory. Subjects like glueballs, topological excitations, and approaches like chiral p- turbation theory are mentioned only brie?y. This allows us to cover the other topics quite explicitly, including detailed derivations of key equations. The ?eld is rapidly developing. The proceedings of the annual lattice conferences provide information on newer directions and up-to-date results.Trade ReviewFrom the reviews:“This is a very nice and readable book on lattice gauge theories. It is conceived for non-specialists in the field and is quite self-contained. … It is a modern, updated introduction to lattice gauge theory, very easy to consult and conceived in a modern way. This is an excellent textbook for students or anyone wishing to be introduced to the subject.” (Giuseppe Nardelli, Mathematical Reviews, Issue 2010 k)Table of ContentsThe path integral on the lattice.- The path integral on the lattice.- QCD on the lattice — a first look.- QCD on the lattice — a first look.- Pure gauge theory on the lattice.- Pure gauge theory on the lattice.- Numerical simulation of pure gauge theory.- Numerical simulation of pure gauge theory.- Fermions on the lattice.- Fermions on the lattice.- Hadron spectroscopy.- Hadron spectroscopy.- Chiral symmetry on the lattice.- Chiral symmetry on the lattice.- Dynamical fermions.- Dynamical fermions.- Symanzik improvement and RG actions.- Symanzik improvement and RG actions.- More about lattice fermions.- More about lattice fermions.- Hadron structure.- Hadron structure.- Temperature and chemical potential.- Temperature and chemical potential.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Die Relativitätstheorie Einsteins
Book SynopsisDieses Buch ist bis heute eine der populärsten Darstellungen der Relativitätstheorie geblieben. In der vorliegenden Version haben J. Ehlers und M. Pössel vom Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) in Golm/Potsdam den Bornschen Text kommentiert und einen den anschaulichen, aber präzisen Stil Borns wahrendes, umfangreiches Ergänzungskapitel hinzugefügt, das die stürmische Entwicklung der Relativiatätstheorie bis hin zu unseren Tagen nachzeichnet. Eingegangen wird auf Gravitationswellen und Schwarze Löcher, auf neuere Entwicklungen der Kosmologie, auf Ansätze zu einer Theorie der Quantengravitation und auf die zahlreichen raffinierten Experimente, welche die Gültigkeit der Einsteinschen Theorie mit immer größerer Genauigkeit bestätigt haben. Damit bleibt dieses Buch nach wie vor einer der unmittelbarsten Zugänge zur Relativitätstheorie für alle die sich für eine über das rein populärwissenschaftliche hinausgehende Einführung interessieren.Trade Review"Allen interessierten Laien sehr zu empfehlen, die ohne höhere Mathematik tiefer in diese Materie eindringen möchten." (Weltraum-Facts mit Space-Informer, 2001) "Alle, die sich über eine rein populärwissenschaftliche Einführung hinaus für die Relativitätstheorie interessieren – besonders Physikstudenten – werden an dem eingehenden Werk Freude haben." (Der Sternenbote, 2001) "Die Erweiterung bereichert den Text von Born aber nicht nur um neuere Entwicklungen der Physik. Rückverweise verzahnen die neuen Kapitel inhaltlich mit den vorstehenden Überlegungen, und auch das Bornsche Projekt, für den mit Schulmathemaitk und einem "gesunden Menschenverstand" ausgestatteten Leser verständlich zu sein, wird erfolgreich fortgeführt." (Wissenschaftlicher Literaturanzeiger, 2001) "Das Buch zeichnet sich in besonderm Maße gegenüber fast allen anderen Abhandlungen über dieses Thema dadurch aus, daß es in einer zuweilen geradezu brillianten Ausdrucksweise die Problematik der klassischen Physik und deren Hintergrund aufzeigt, die dann durch Einsteins Theorien eine Auflösung fand. [...] Alles in allem ein sehr lesenswertes Buch, jedoch kein populärwissenschaftliches und für den Laien sicherlich auch kein leichtes. Denn trotz der außerordentlich gut verständlichen Darstellungsweise Borns erfordert das Buch außer etwas Grundlagen-Mathematik ein hohes Maß an Aufmerksamkeit und die bereitschaft, physikalsiche Sachverhalte gedanklich zu durchdringen. Es ist mit sicherheit ein Verdienst von Herausgebern und Verlag, Borns Buch durch die Neuauflage mit den aktuellen Ergänzungen wieder einer interessierten Leserschaft verfügbar zu machen." (Nachrichten der Olbers-Gesellschaft, 2001) "Wer eine fundierte, gründliche Einführung in die Welt der Relativitätstheorie sucht, kommt an Borns Klassiker nicht vorbei. Freilich muß man sich mitunter bemühen und auch einiges an Mathematik bewältigen, läuft dafür aber nicht Gefahr, durch aus dem Alltag entlehnte Analogien verwirrt zu werden." (Sirius – Zeitschrift der Vereinigten Amateur-Astronomen, 2002) "Wer die populärwissenschaftlichen Darstellungen der Relativitätstheorie als nicht ausreichend betrachtet und gern etwas tiefer schürfen möchte, dem sei dieses Buch als Lektüre ans Herz gelegt." (Astrokurier, 2002) "Ehlers und Pössel ist damit ein gelungenes Remake von Borns wegweisendem Werk gelungen. Sie haben bewiesen, dass der 80 Jahre alte Zugang zu Einsteins Theorie auch heute noch gangbar ist." (Physik in unserer Zeit, 2002) "[...] weiterhin einer der unmittelbarsten Zugänge zur Relativitätstheorie für Schüler-, Lehrer- und Studentenschaft sowie für alle, die sich nicht beruflich mit relativistischer Physik beschäftigen möchten, insbesondere für jene Leserschaft aus der Amateur-Astronomie, die an einem tieferen Verständnis dieses spannenden Themas interessiert ist. Gerade diesem Kreis ist das vorliegende Buch als Einführung in die moderne Kosmologie sehr zu empfehlen." (ORION 61/314, 2003)Table of ContentsGeometrie und Kosmologie.- Die Grundgesetze der klassischen Mechanik.- Das Newtonsche Weltsystem.- Die Grundgesetze der Optik.- Die Grundgesetze der Elektrodynamik.- Das spezielle Einsteinsche Relativitätsprinzip.- Die allgemeine Relativitätstheorie Einsteins.- Neuere Entwicklungen der relativistischen Physik.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers II: PDE, SDE, Diffusions, Random
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume II includes the papers on PDE, SDE, diffusions, and random media.Table of ContentsVol. II: Diffusion processes with continuous coefficients - I (with D. W. Stroock).- Diffusion processes with continuous coefficients - II (with D. W. Stroock).- Diffusion processes with boundary conditions (with D. W. Stroock).- On degenerate elliptic-parabolic operators of second order and their associated diffusions (with D. W. Stroock).- On the support of diffusion processes with applications to the strong maximum principle (with D. W. Stroock).- Diffusion processes (with D. W. Stroock).- A probabilistic approach to Hp(Rd) (with D. W. Stroock).- Kac functional and Schrodinger equation (with K. L. Chung).- Brownian motion in a wedge with oblique reection (with R. J. Williams).- A multidimensional process involving local time (with A.S. Sznitman).- Etat fondamental et principe du maximum pour les operateurs elliptiques du second ordre dans des domaines generaux. [The ground state and maximum principle for second-order elliptic operators in general domains] (with H. Berestycki and L. Nirenberg).- The principal eigenvalue and maximum principle for second-order elliptic operators in general domains (with H. Berestycki and L. Nirenberg).- Diffusion semigroups and di_usion processes corresponding to degenerate divergence form operators (with J. Quastel).- Random Media.- Diffusion in regions with many small holes (with G. Papanicolaou).- Boundary value problems with rapidly oscillating random coefficients (with G. Papanicolaou).- Diffusions with random coefficients (with G. Papanicolaou).- Ohrnstein-Uhlenbeck process in a random potential (with G. Papanicolaou).- Large deviations for random walks in a random environment.- Random walks in a random environment.- Stochastic homogenization of Hamilton-Jacobi-Bellman equations (with E. Kosygina and F. Rezakhanlou).- Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium (with E. Kosygina).- Behavior of the solution of a random semilinear heat equation (with N. Zygouras).
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers III: Large Deviations
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012.Volume III includes the papers on large deviations. Table of ContentsLarge Deviations.- Asymptotic probabilities and differential equations.- On the behavior of the fundamental solution of the heat equation with variable coefficients .- Diffusion processes in a small time interval .- On a variational formula for the principal eigenvalue for operators with maximum principle.- Asymptotic evaluation of certain Markov process expectations for large time I.- Asymptotic evaluation of certain Markov process expectations for large time II.- Asymptotic evaluation of certain Wiener integrals for large time.- Asymptotics for the Wiener sausage.- Erratum: Asymptotics for the Wiener sausage.- Asymptotic evaluation of certain Markov process expectations for large time III.- On the principal eigenvalue of second-order elliptic differential operators.- On laws of the iterated logarithm for local times.- Some problems of large deviations.- On the number of distinct sites visited by a random walk.- A law of the iterated logarithm for total occupation times of transient Brownian motion.- Some problems of large deviations .- The polaron problem and large deviations.- Asymptotic evaluation of certain Markov process expectations for large time IV.- Asymptotics for the polaron.- Large deviations for stationary Gaussian processes.- Large deviations and applications.- Large deviations for non-interacting infinite-particle systems.- Some familiar examples for which the large deviation principle does not hold.- The large deviation principle for the Erdös-Rényi random graph.- Large deviations for random matrices.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers IV: Particle Systems and Their
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume IV includes the papers on particle systems.Table of ContentsVolume 4: Particle Systems and Their Large Deviations.- Nonlinear diffusion limit for a system with nearest neighbor interaction.- Hydrodynamics and large deviation for simple exclusion processes.- Large deviations from a hydrodynamic scaling limit.- On the derivation of conservation laws for stochastic dynamics.- Scaling limits for interacting diffusions.- Scaling limit for interacting Ornstein-Uhlenbeck processes.- Entropy methods in hydrodynamical scaling.- Hydrodynamical limit for a Hamiltonian system with weak noise.- Nonlinear diffusion limit for a system with nearest neighbor interactions II.- Regularity of self-diffusion coefficient.- Entropy methods in hydrodynamic scaling.- Spectral gap for zero-range dynamics.- The complex story of simple exclusion.- Non-gradient models in hydrodynamic scaling.- Relative entropy and mixing properties of interacting particle systems.- Diffusive limit of lattice gas with mixing conditions.- Large deviations for the symmetric simple exclusion process in dimensions d > 3.- Large deviations for interacting particle systems.- Infinite particle systems and their scaling limits.- Lectures on hydrodynamic scaling.- Scaling limits of large interacting systems .- Asymptotic behavior of a tagged particle in simple exclusion processes.- Large deviation and hydrodynamic scaling.- Symmetric simple exclusion process: regularity of the self-diffusion coefficient.- Finite-dimensional approximation of the self-diffusion coefficient for the exclusion process.- Large deviations for the asymmetric simple exclusion process.- Diffusive behaviour of the equilibrium fluctuations in the asymmetric exclusion processes.- On viscosity and fluctuation-dissipation in exclusion processes.- Large deviations for the current and tagged particle in 1d nearest neighbor.- Symmetric simple exclusion.- List of Publications of S.R.S. Varadhan.- Acknowledgements.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Basic Algebraic Geometry 1: Varieties in Projective Space
Book SynopsisShafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles.Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.Trade Review“This is a very good book and very good introduction to algebraic geometry and it serves an entry door to this enormous subject in mathematics. … This book is classical and I strongly recommend it as the first book on algebraic geometry. … It is an excellent book and every mathematician should have a copy.” (Philosophy, Religion and Science Book Reviews, Bookinspections.wordpress.com, July, 2016)“I find the book wonderfully put together, and I am sure the reader will learn a lot, either from systematic study or from browsing particular topics. … In each chapter, the theorems, propositions, corollaries, examples, remarks, etc., each have their own independent numbering system, running consecutively throughout the chapter. This makes it a real chore to track any internal reference in the book.” (Robin Hartshorne, SIAM Review, Vol. 56 (4), December, 2014)“The author’s two-volume textbook ‘Basic Algebraic Geometry’ is one of the most popular standard primers in the field. … the author’s unique classic is a perfect first introduction to the geometry of algebraic varieties for students and nonspecialists, and the current, improve third edition will maintain this outstanding role of the textbook in the relevant literature without any doubt.” (Werner Kleinert, zbMATH, Vol. 1273, 2013)Table of ContentsPreface.- Book 1. Varieties in Projective Space: Chapter 1. Basic Notions.- Chapter II. Local Properties.- Chapter III. Divisors and Differential Forms.- Chapter IV. Intersection Numbers.- Algebraic Appendix.- References.- Index
£75.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Springer Handbook of Spacetime
Book SynopsisThe Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects.The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.Trade Review“This is a complete comprehensive textbook of all areas of classical and relativistic Physics including mechanics, E & M, quantum theory, perturbation, solid state, and particle physics. … It is good enough to be read cover to cover and will not disappoint the reader reviewer. I highly recommend this book for physics students, and investigators in physics theories.” (Joseph J. Grenier, Amazon.com, January, 2016)“This is a splendid and very comprehensive review of the special and general theories of relativity and their applications, in a collection of about 40 articles by experts in the field. … the book will appeal to a wide variety of readers, from advanced undergraduates to experts in the field. … I doubt that there is any physicist who would not find something new and interesting here.” (Alan Heavens, The Observatory, Vol. 135 (1245), April, 2015)Table of ContentsPreface (A. Ashtekar, V. Petkov).- Part A – Introduction to Spacetime Structure.- Chap. 1 From Aether Theory to Special Relativity.- Chap. 2 The Historical Origins of Spacetime.- Chap. 3 Relativity Today.- Chap. 4 Acceleration and Gravity: Einstein's Principle.- Chap. 5 The Geometry of Newton's and Einstein's Theories.- Part B – Foundational Issues.- Chap. 6 Time in Special Relativity.- Chap. 7 Rigid Motion and Adapted Frames.- Chap. 8 Physics as Spacetime Geometry.- Chap. 9 Electrodynamics of Radiating Charges.- Chap. 10 The Nature and Origin of Time-Asymmetric Spacetime Structures.- Chap. 11 Teleparallelism: A new Insight into Gravity.- Chap. 12 Gravity and the Spacetime: An Emergent Perspective.- Chap. 13 Spacetime and the Passage of Time.- Part C – Spacetime Structure and Mathematics.- Chap. 14 Unitary Representations of the Inhomogeneous Lorentz Group and Their Significance in Quantum Physics.- Chap. 15 Spinors.- Chap. 16 The Initial Value Problem in General Relativity.- Chap. 17 Dynamical and Hamiltonian Formulation of General Relativity.- Chap. 18 Positive Energy Theorems in General Relativity.- Chap. 19 Conserved Charges in Asymptotically (Locally) AdS Spacetimes.- Chap. 20 Spacetime Singularities.- Chap. 21 Singularities in Cosmological Spacetimes.- Part D – Confronting Relativity theories with observations.- Chap. 22 The experimental status of Special and General Relativity Chap. 23. Observational Constraints on Local Lorentz Invariance.- Chap. 24 Relativity in GNSS.- Chap. 25 Quasi Local Black Hole Horizons.- Chap. 26 Gravitational Astronomy.- Chap. 27 Probing Dynamical Spacetimes with Gravitational Waves.- Part E – General Relativity and the Universe.- Chap. 28 Einstein's Equation, Cosmology and Astrophysics.- Chap. 29 Viscous Universe Models.- Chap. 30 Friedmann-Lemaitre-Robertson-Walker Cosmology.- Chap. 31 Exact Approach to Inflationary Universe Models.- Chap. 32 Cosmology with the Cosmic Microwave Background.- Part F – Spacetime Beyond Einstein.- Chap. 33 Quantum Gravity.- Chap. 34 Quantum Gravity via Causal Dynamical Triangulations.- Chap. 35 String Theory and Primordial Cosmology.- Chap. 36 Quantum Spacetime.- Chap. 37 Gravity, Geometry and the Quantum.- Chap. 38 Spin Foams.- Chap. 39 Loop Quantum Cosmology.- Acknowledgements.- About the Authors.- Subject Index.
£251.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Concepts and Results in Chaotic Dynamics: A Short Course
Book SynopsisThe study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.Trade ReviewFrom the reviews: "The book is a good introduction to the field of dynamical systems with a particular emphasis on statistical properties and applications. In particular, the relations both with real experiments with numerical simulations are discussed. … The book contains many figures that really help the understanding of the text. The book can be used as a text for an introductory course in dynamical systems (at the master’s or Ph.D. level). It is particularly suited for students with interests in applications (either physics, economy or biology)." (Carlangelo Liverani, Mathematical Reviews, Issue 2007 m) "Two thoughts crossed my mind when I picked up this book. The first was: ‘what a physically attractive book.’ The second was: ‘what a short book to have on such a wide ranging topic.’ … It is a perfect size to carry in a knapsack, the print is clear and the layout of text, equations, and figures is marvelously done. … images are multi-colored stereo images, and allow the reader to ‘see’ a three dimensional effect that helps illustrate the phenomena." (David S. Mazel, MathDL, December, 2007)Table of ContentsA Basic Problem.- Dynamical Systems.- Topological Properties.- Hyperbolicity.- Invariant Measures.- Entropy.- Statistics and Statistical Mechanics.- Other Probabilistic Results.- Experimental Aspects.
£40.49
