Mathematical / Computational / Theoretical physics Books
Springer International Publishing AG Cosmic Rays: Multimessenger Astrophysics and
Book SynopsisIn recent years, cosmic rays have become the protagonists of a new scientific revolution. We are able today to film the Universe with telescopes of completely novel conception, recording information from many different messengers and accessing previously unknown cosmic regions.Written by a recognized authority in physics, this book takes readers on a captivating journey through the world of cosmic rays, their role in the revolutionary field of multi-messenger astronomy, their production from powerful accelerators close to the surfaces of black holes and compact objects, reaching the highest levels of energy observed in nature, and the implications this has for our understanding of the Universe. Through the stories of pioneering scientists, explorations of cutting-edge technologies, and simple explanations related to particle physics, quantum mechanics, and astrophysics, the book provides an illuminating state-of-the-art introduction to the current state of high-energy astrophysics. The book was written in straightforward yet rigorous language, so as to be accessible to the greater public. For those curious about the cosmos and cosmic gamma rays, nuclei, neutrinos, and gravitational waves, from casual observers to professional astronomers and physicists, the book is a must-read, offering a thrilling adventure into the future of astronomy and particle physics.Table of ContentsIntroduction 1 The Largest Energies in the Universe 1.1 The Universe around us 1.2 Particles and fields 1.3 Cosmic rays 2 The Mystery of Cosmic Rays 2.1 The discovery of natural radioactivity 2.2 Is natural radioactivity of extraterrestrial origin? 2.3 Father Wulf, a true experimental physicist 2.4 Pacini’s attenuation measures in water 2.5 Hess and balloon measurements 2.6 First developments and the tragedy of the first world war 3 Cosmic-Ray Research after the First World War 3.1 Research in Europe and the Pacini-Hess controversy 3.2 Research in the United States 3.3 Are cosmic rays predominantly charged or neutral? 3.4 Bruno Rossi and the discoveries after 1930 3.5 At the origins of elementary particle physics 3.6 The recognition of the scientific community 3.7 Hypothesis on the origin of cosmic rays: Tesla, Zwicky, Fermi 4 Cosmic Rays and the Physics of Elementary Particles 4.1 Leptons and mesons 4.2 The neutral pion 4.3 The discovery of strangeness 4.4 Laboratories on the mountains 4.5 Hunters become shepherds: particle accelerators 5 Fire Under the Ashes: the Discoveries at the End of the 20th Century and at the Beginning of the 21st Century 5.1 Cosmic rays of very-high-energy 5.2 Anomalous events 5.3 X-rays 5.4 Neutrinos from the Sun and the cosmos 6 Cosmic Ray Research Today: Multi-Messenger Astrophysics and the New Astronomy 6.1 Very-high-energy cosmic rays 6.2 Search for antimatter 6.3 Gamma rays 6.4 Cosmic neutrinos 6.5 Gravitational waves 6.6 Multi-messenger astronomy 7 Cosmic Rays and Climate 7.1 Cosmic rays and thunderstorms 7.2 Variations in the flux of cosmic rays 7.3 A correlation between cosmic rays and earthquakes? 8 Cosmic Rays and Life 8.1 Ionization and chemistry of the atmosphere 8.2 The Miller-Urey experiment 8.3 Biological effects of cosmic rays 8.4 Implications on evolution 9 Cosmic Rays and the Exploration of the Universe 10 Cosmic Rays and Archaeology 10.1 Dating techniques 10.2 Muon tomography 11 The Future
£26.59
Springer International Publishing AG Instabilities in Field Theory: A Primer with Applications in Modified Gravity
Book SynopsisThis book presents the most common types of instabilities arising in classical field theories, namely tachyonic, Laplacian, ghost-like or strong coupling instabilities, also commenting on their quantum implications. The authors provide a detailed account on the Ostrogradski theorem and its implications for higher-order time-derivative field theories. After presenting the general concepts and formalism, they dive into its applications to particular field theories, using mainly modified gravity theories as examples. The book is intended for advanced undergraduate/graduate students, but can also be useful for researchers, for having a unified exposition of general results on instabilities in field theory and examples of their applications.Table of ContentsIntroduction to instabilities and some relevant examples.- Ostrogradski theorem and ghosts.- Examples of instabilities in gravity theories.- References.- Solutions.
£33.24
Springer Analytical Mechanics
Book Synopsis
£71.24
Springer Nonlinear FokkerPlanck Flows and their
Book Synopsis- Introduction.- Existence of nonlinear FokkerPlanck flows.- Time dependent FokkerPlanck equations.- Convergence to equilibrium of nonlinear FokkerPlanck flows.- Markov processes associated with nonlinear FokkerPlanck equations.- Appendix.
£49.49
Springer International Publishing AG Linear Algebra for Physics
Book SynopsisAlthough the mathematical level is similar to the corresponding mathematical textbooks in regard to definitions, propositions and proofs, it adopts a language and approach more attuned to the reader's familiarity with physics lectures and physics textbooks.
£71.24
Springer Geometry Topology and Operator Algebras
Book SynopsisGeometric structures, invariants and their uses in physics by A. Cardona and A.F. Reyes-Lega.- . Lectures on the Euler characteristic of affine manifolds by Camilo Arias-Abad and Sebastian Velez-Vasquez.- Elliptic Curves by Philip Candelas.- The arithmetic of Calabi-Yau varieties, by Xenia de la Ossa.- Foliations and operator algebras by Georges Skandalis.- Pseudo-differential operators on groups and nonharmonic analysis, by Michael Ruzhansky.- Mathematical Foundations of Topological Matter, by Manuel Asorey.
£62.99
Walter de Gruyter Gravitation und Relativität
Book Synopsis
£33.20
De Gruyter The HodgeLaplacian
Book Synopsis
£139.17
de Gruyter Instationäre Schwingungen Mechanischer Systeme
Book Synopsis
£126.64
Springer International Publishing AG Numerical Modelling of Astrophysical Turbulence
Book SynopsisIn this "SpringerBrief" the author considers the underlying problems and questions that are common to numerical models of turbulence in different astrophysical systems. Turbulence has emerged as an important research topic in several areas of astrophysics. Understanding and modeling turbulence is particularly important for the dynamics of the interstellar medium, but also for the intergalactic medium, as well as in stars. The advancement of methods for numerical simulations of astrophysical turbulence, however, is still challenging because of gravity, strong compressibility, magnetic fields, and other effects.The book begins with a review of general aspects of numerical simulations of turbulence. In the main part the author presents findings from his numerical studies on astrophysical turbulence and discusses the astrophysical implications. He also explains in detail the numerical schemes utilized.Readers will find that this book offers a compact yet comprehensive introduction.Trade Review“This book provides an interesting and well-written account on an area witnessing encouraging progress.” (H. Muthsam, Monatshefte für Mathematik, 2016)“The primary focus of this book is on the numerical methods and their application in studying the fundamental statistical properties of compressible hydrodynamic turbulence. … The book can be a useful survey and reference source for researchers in the field. Also, it can be a good point of introduction for someone wanting to develop a research capability in this area.” (Stephen Wollman, zbMATH 1317.85004, 2015)Table of ContentsTurbulence theory.- Simulation techniques.- Phenomenology and statistics.- Complex processes.
£42.74
Springer International Publishing AG The Cellular Automaton Interpretation of Quantum Mechanics
Book SynopsisThis book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft.Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory.The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.Table of ContentsI The Cellular Automaton Interpretation as a general doctrine: Motivation for this work.- Deterministic models in quantum notation.- Interpreting quantum mechanics.- Deterministic quantum mechanics.- Concise description of the CA Interpretation.- Quantum gravity.- Information loss.- More problems.- Alleys to be further investigated and open questions.- Conclusions.- II Calculation Techniques: Introduction to part II.- More on cogwheels.- The continuum limit of cogwheels, harmonic rotators and oscillators.- Locality.- Fermions.- PQ theory.- Models in two space-time dimensions without interactions.- Symmetries.- The discretised Hamiltonian formalism in PQ theory.- Quantum Field Theory.- The cellular automaton.- The problem of quantum locality.- Conclusions of part II.- Some remarks on gravity in 2+1 dimensions.- A summary of our views on Conformal Gravity.- Abbreviations.
£42.74
Springer International Publishing AG Quantum Theory, Groups and Representations: An Introduction
Book SynopsisThis text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.Trade Review“The book presents a large variety of important subjects, including the basic principles of quantum mechanics … . This good book is recommended for mathematicians, physicists, philosophers of physics, researchers, and advanced students in mathematics and physics, as well as for readers with some elementary physics, multivariate calculus and linear algebra courses.” (Michael M. Dediu, Mathematical Reviews, June, 2018)Table of ContentsPreface.- 1 Introduction and Overview.- 2 The Group U(1) and its Representations.- 3 Two-state Systems and SU(2).- 4 Linear Algebra Review, Unitary and Orthogonal Groups.- 5 Lie Algebras and Lie Algebra Representations.- 6 The Rotation and Spin Groups in 3 and 4 Dimensions.- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field.- 8 Representations of SU(2) and SO(3).- 9 Tensor Products, Entanglement, and Addition of Spin.- 10 Momentum and the Free Particle.- 11 Fourier Analysis and the Free Particle.- 12 Position and the Free Particle.- 13 The Heisenberg group and the Schrödinger Representation.- 14 The Poisson Bracket and Symplectic Geometry.- 15 Hamiltonian Vector Fields and the Moment Map.- 16 Quadratic Polynomials and the Symplectic Group.- 17 Quantization.- 18 Semi-direct Products.- 19 The Quantum Free Particle as a Representation of the Euclidean Group.- 20 Representations of Semi-direct Products.- 21 Central Potentials and the Hydrogen Atom.- 22 The Harmonic Oscillator.- 23 Coherent States and the Propagator for the Harmonic Oscillator.- 24 The Metaplectic Representation and Annihilation and Creation Operators, d = 1.- 25 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d.- 26 Complex Structures and Quantization.- 27 The Fermionic Oscillator.- 28 Weyl and Clifford Algebras.- 29 Clifford Algebras and Geometry.- 30 Anticommuting Variables and Pseudo-classical Mechanics.- 31 Fermionic Quantization and Spinors.- 32 A Summary: Parallels Between Bosonic and Fermionic Quantization.- 33 Supersymmetry, Some Simple Examples.- 34 The Pauli Equation and the Dirac Operator.- 35 Lagrangian Methods and the Path Integral.- 36 Multi-particle Systems: Momentum Space Description.- 37 Multi-particle Systems and Field Quantization.- 38 Symmetries and Non-relativistic Quantum Fields.- 39 Quantization of Infinite dimensional Phase Spaces.- 40 Minkowski Space and the Lorentz Group.- 41 Representations of the Lorentz Group.- 42 The Poincaré Group and its Representations.- 43 The Klein-Gordon Equation and Scalar Quantum Fields.- 44 Symmetries and Relativistic Scalar Quantum Fields.- 45 U(1) Gauge Symmetry and Electromagnetic Field.- 46 Quantization of the Electromagnetic Field: the Photon.- 47 The Dirac Equation and Spin-1/2 Fields.- 48 An Introduction to the Standard Model.- 49 Further Topics.- A Conventions.- B Exercises.- Index.
£57.59
Springer International Publishing AG Foundations of Quantum Theory: From Classical
Book SynopsisThis book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.This book is Open Access under a CC BY licence. Trade Review“Quantum theory has frequent applications in the subjects of quantum information theory and quantum optics. The purpose of this book is to present the foundations of quantum theory in connection with classical physics, from the point of view of classical-quantum duality. … This good book is recommended for mathematicians, physicists, philosophers of physics, researchers and advanced students in this field.” (Michael M. Dediu, Mathematical Reviews, Decemeber, 2017)Table of ContentsIntroduction.- Part I Co(X) and B(H): Classical physics on a finite phase space.- Quantum mechanics on a finite-dimensional Hilbert space.- Classical physics on a general phase space.- Quantum physics on a general Hilbert space.- Symmetry in quantum mechanics.- Part II Between Co(X) and B(H): Classical models of quantum mechanics.- Limits: Small hbar.- Limits: large N.- Symmetry in algebraic quantum theory.- Spontaneous Symmetry Breaking.- The Measurement Problem.- Topos theory and quantum logic.- Appendix A: Finite-dimensional Hilbert spaces.- Appendix B: Basic functional analysis.- Appendix C: Operator algebras.- Appendix D: Lattices and logic.- Appendix E: Category theory and topos theory.- References.
£42.74
Springer International Publishing AG Quantum Theory, Groups and Representations: An Introduction
Book SynopsisThis text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.Trade Review“The book presents a large variety of important subjects, including the basic principles of quantum mechanics … . This good book is recommended for mathematicians, physicists, philosophers of physics, researchers, and advanced students in mathematics and physics, as well as for readers with some elementary physics, multivariate calculus and linear algebra courses.” (Michael M. Dediu, Mathematical Reviews, June, 2018)Table of ContentsPreface.- 1 Introduction and Overview.- 2 The Group U(1) and its Representations.- 3 Two-state Systems and SU(2).- 4 Linear Algebra Review, Unitary and Orthogonal Groups.- 5 Lie Algebras and Lie Algebra Representations.- 6 The Rotation and Spin Groups in 3 and 4 Dimensions.- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field.- 8 Representations of SU(2) and SO(3).- 9 Tensor Products, Entanglement, and Addition of Spin.- 10 Momentum and the Free Particle.- 11 Fourier Analysis and the Free Particle.- 12 Position and the Free Particle.- 13 The Heisenberg group and the Schrödinger Representation.- 14 The Poisson Bracket and Symplectic Geometry.- 15 Hamiltonian Vector Fields and the Moment Map.- 16 Quadratic Polynomials and the Symplectic Group.- 17 Quantization.- 18 Semi-direct Products.- 19 The Quantum Free Particle as a Representation of the Euclidean Group.- 20 Representations of Semi-direct Products.- 21 Central Potentials and the Hydrogen Atom.- 22 The Harmonic Oscillator.- 23 Coherent States and the Propagator for the Harmonic Oscillator.- 24 The Metaplectic Representation and Annihilation and Creation Operators, d = 1.- 25 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d.- 26 Complex Structures and Quantization.- 27 The Fermionic Oscillator.- 28 Weyl and Clifford Algebras.- 29 Clifford Algebras and Geometry.- 30 Anticommuting Variables and Pseudo-classical Mechanics.- 31 Fermionic Quantization and Spinors.- 32 A Summary: Parallels Between Bosonic and Fermionic Quantization.- 33 Supersymmetry, Some Simple Examples.- 34 The Pauli Equation and the Dirac Operator.- 35 Lagrangian Methods and the Path Integral.- 36 Multi-particle Systems: Momentum Space Description.- 37 Multi-particle Systems and Field Quantization.- 38 Symmetries and Non-relativistic Quantum Fields.- 39 Quantization of Infinite dimensional Phase Spaces.- 40 Minkowski Space and the Lorentz Group.- 41 Representations of the Lorentz Group.- 42 The Poincaré Group and its Representations.- 43 The Klein-Gordon Equation and Scalar Quantum Fields.- 44 Symmetries and Relativistic Scalar Quantum Fields.- 45 U(1) Gauge Symmetry and Electromagnetic Field.- 46 Quantization of the Electromagnetic Field: the Photon.- 47 The Dirac Equation and Spin-1/2 Fields.- 48 An Introduction to the Standard Model.- 49 Further Topics.- A Conventions.- B Exercises.- Index.
£57.59
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Chaos und Systeme: Eine Einführung in Theorie und
Book SynopsisDieses Buch ist eine besonders geeignete Einführung zum Thema Chaos und Simulation dynamischer Systeme für Studenten der Ingenieur- und der Naturwissenschaften. Die Untersuchung von einfachen Modellen aus der Populationsdynamik dient als Vehikel, einen schnellen und zielgerichteten Einstieg zu erzielen. Das nötige mathematische und simulationstechnische Werkzeug wird nach Bedarf eingeführt und gut verständlich erklärt. Unterstützt wird die Darstellung durch Programme auf beiliegender Diskette, die die Zusammenhänge verdeutlichen und zum Experimentieren anregen.Table of ContentsPopulationsdynamik - Räuber-Beute-Systeme - Simulation nichtlinearer Differentialgleichungen - Prozeßorientierte Simulation - Stabilität - Bifurkation - seltsame Attraktoren - Chaos - dissipative Systeme - fraktale Ddimension - Lorenzmodelle - Dynamik der Krankheitsepidemien
£31.34
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Mechanik
Book SynopsisMathematische Grundlagen - Kinematik - Dynamik - Statik starrer Systeme - Statik deformierbarer Systeme - Kinetik starrer Systeme - Kinetik deformierbarer Systeme - Prinzipien der Mechanik.Trade Review,,(...) Vor allem auch aufgrund der systematisch gegliederten Darstellung sowie der klar formulierten Aussagen kann dieses Buch allen Studenten, Naturwissenschaftlern und Ingenieuren sehr empfohlen werden, die sich in die Grundlagenwissenschaft 'Mechanik' einarbeiten wollen und/oder die diese als ein wertvolles Instrument zum Lösen technischer Probleme benötigen."VDI-Z 18/1986Table of ContentsMathematische Grundlagen - Kinematik - Dynamik - Statik starrer Systeme - Statik deformierbarer Systeme - Kinetik starrer Systeme - Kinetik deformierbarer Systeme - Prinzipien der Mechanik.
£47.49
Springer Fachmedien Wiesbaden Teubner-Taschenbuch der statistischen Physik
Book SynopsisAus moderner Sicht werden in diesem Teubner-Taschenbuch die Grundlagen und wichtige Anwendungen der statistischen Physik dargestellt. Auf eine gründliche Darstellung der Begriffsbildungen der statistischen Physik, auf die korrekte Herleitung grundlegender Gleichungen und auf die Durchführung wichtiger Beweise wird besonderer Wert gelegt. Das Buch eignet sich als Begleittext für Kurs- und Spezialvorlesungen, als Repetitorium zur Prüfungsvorbereitung und als Nachschlagewerk zur raschen Information für breite Leserkreise aus Mathematik, Naturwissenschaften und technischen Disziplinen, insbesondere für Studenten dieser Fachrichtungen.Table of ContentsKombinatorik - Wahrscheinlichkeitstheorie - Quantenmechanik und Wahrscheinlichkeit - Thermodynamik - Statistische Physik der Gleichgewichtssysteme - Statistische Physik der Systeme im Nichtgleichgewicht - Statistische Physik und Informationstheorie - Phasenraummethoden der Quantenstatistik - Fraktaltheorie und Perkolationstheorie - Theorie dynamischer Systeme, Chaostheorie, Ergodentheorie - Statistische Thermodynamik chemischer Systeme - Statistische Theorie biologischer Systeme - Synergetik, weitere Anwendungen der statistischen Physik
£49.49
Springer Fachmedien Wiesbaden Elektromagnetische Feldtheorie: Eine
Book SynopsisZusammen mit einer kurzen Einführung in das System der Maxwellschen Gleichungen und einer Definition der Feldgrößen lehrt das Buch mit charakteristischen Beispielen die Lösungsmethodik der Feldtheorie. Schwerpunkte sind dabei statistische und stationäre elektrische und magnetische Felder, quasistationäre elektromagnetische Felder und elektromagnetische Wellen. Für das Verständnis besonders hilfreich ist die Darstellung von Feldlinienbildern. Dieses Lehrbuch bietet eine Sammlung ausgewählter anspruchsvoller Übungsaufgaben mit Lösungen, die es ermöglichen, die elektromagnetische Feldtheorie zu verstehen und sachgerecht anzuwenden.Trade Review"Das Buch enthält in untadeliger Darstellung etliche Aufgaben mit Ausarbeitung zu den klassischen Teilgebieten der Elektrodynamik, wobei die ausgezeichneten Feldbilder besonders hervorgehoben werden müssen. Den zitierten Wunsch des Autors hat sich dieser mit seinem Buch ohne Frage erfüllt." Impulse, 01/2003Table of ContentsDie Maxwellschen Gleichungen - Elektrostatische Felder - Das stationäre Strömungsfeld - Das magnetische Feld stationärer Ströme - Das quasistationäre elektromagnetische Feld: der Skineffekt - Elektromagnetische Wellen
£31.34
Springer Fachmedien Wiesbaden Einführung in die mathematischen Methoden der
Book SynopsisTable of Contents1. Mathematische Grundlagen.- 1.1. Der Begriff des Feldes und des Gradienten.- 1.1.1. Definition der Feldgröße.- 1.1.2. Änderung (Differentiation) der Feldgrößen.- 1.2. Integration der Feldgrößen.- 1.2.1. Kurvenintegrale.- 1.2.2. Flächenintegrale.- 1.3. Tensoren.- 1.3.1. Der Begriff des Tensorfeldes.- 1.3.2. Rechenregeln für Tensoren in kartesischen Koordinatensystemen.- 1.3.3. Der 5-Tensor und e-Tensor.- 1.4. Koordinatentransformationen.- 1.5. Einfachste Differentialoperatoren.- 1.5.1. Die Divergenz und der Satz von Gauß.- 1.5.2. Die Rotation und der Satz von Stokes.- 1.5.3. Sprungflächenoperatoren.- 1.5.4. Divergenz und Rotor in krummlinigen Koordinaten.- 1.6. Übungsbeispiele zu Kap. 1.- 2. Partielle Differentialgleichungen der Physik.- 2.1. Die Poissonsche Differentialgleichung.- 2.1.1. Beschreibung eines Feldes durch Quellen und Wirbel.- 2.1.2. Eindeutigkeit der Lösung. Randbedingungen.- 2.2. Die partielle Differentialgleichung von Schwingungsvorgängen.- 2.2.1. Die schwingende Saite.- 2.2.2. Die schwingende Membran und räumliche Schwingungen.- 2.3. Die Differentialgleichungen der Diffusion und Wärmeleitung.- 2.4. Einfachste Differentialgleichungen der Quantenmechanik.- 2.5. Übungsbeispiele zu Kap. 2.- 3. Lösungsansätze für partielle Differentialgleichungen.- 3.1. Trennung der Variablen.- 3.2. Die Laplacegleichung.- 3.2.1. Die Laplacegleichung für ein Rechteck.- 3.2.2. Die Laplacegleichung in Polarkoordinaten.- 3.3. Die schwingende Saite.- 3.3.1. Die beidseitig eingespannte schwingende Saite.- 3.3.2. Die d’Alembertsche Lösung der schwingenden Saite.- 3.4. Übungsbeispiele zu Kap. 3.- 4. Rand und Eigenwertaufgaben.- 4.1. Problemstellung.- 4.2. Sturm-Liouville-Differentialoperatoren.- 4.2.1. Selbstadjungierte Differentialoperatoren.- 4.2.2. Sturm-Liouville-Randwertaufgaben.- 4.2.3. Sturm-Liouville-Eigenwertaufgaben.- 4.2.4. Die Sturm-Liouville -Transformation.- 4.3. Der Entwicklungssatz.- 4.3.1. Eigenwerte und Eigenfunktionen.- 4.3.2. Der Entwicklungssatz für beschränkte Intervalle.- 4.4. Die Lösung der Anfangsrandwertaufgabe.- 4.5. Die inhomogene Randwertaufgabe.- 4.6. Nadelartige Funktionen.- 4.7. Ergänzungen und Bemerkungen.- 4.8. Übungsbeispiele zu Kap. 4.- 5. Singuläre Differentialgleichungen.- 5.1. Der Begriff der singulären Differentialgleichung. Differentialgleichungen der Fuchsschen Klasse.- 5.2. Die hypergeometrische Differentialgleichung.- 5.3. Die konfluente hypergeometrische Differentialgleichung.- 5.4. Übungsbeispiele zu Kap. 5.- 6. Spezielle Funktionen.- 6.1. Kugelfunktionen.- 6.1.1. Die Laplacegleichung in Kugelkoordinaten.- 6.1.2. Die Legendreschen Polynome und ihre erzeugende Funktion.- 6.1.3. Die Formel vom Rodrigues.- 6.1.4. Die Integraldarstellung von Laplace.- 6.1.5. Die zugeordneten Legendreschen Funktionen.- 6.1.6. Kugelflächenfunktionen als Eigenfunktionen.- 6.1.7. Das Additionstheorem der Kugelflächenfunktionen.- 6.1.8. Der Entwicklungssatz nach Kugelflächenfunktionen.- 6.1.9. Die Randwertaufgaben der Potentialtheorie.- 6.2. Zylinderfunktionen.- 6.2.1. Die Laplacegleichung in Zylinderkoordinaten.- 6.2.2. Besselfunktionen.- 6.2.3. Besselfunktionen als Eigenfunktionen.- 6.2.4. Integraldarstellung und erzeugende Funktion der Besselfunktion Jn (?).- 6.2.5. Das Additionstheorem der Besselfunktionen mit ganzzahligem Zeiger.- 6.2.6. Die Wellengleichung. Sphärische Besselfunktionen.- 6.2.7. Entwicklung einer ebenen Welle nach Kugelwellen.- 6.2.8. Asymptotische Darstellungen für sphärische Besselfunktionen.- 6.3. Hermitesche und Laguerresche Polynome.- 6.3.1. Der harmonische Oszillator (Hermitesche Polynome).- 6.3.2. Die erzeugende Funktion der Hermiteschen Polynome.- 6.3.3. Die Schrödingergleichung für das Wasserstoffatom (Laguerresche Polynome).- 6.4. Übungsbeispiele zu Kap. 6.- 7. Verallgemeinerte Funktionen.- 7.1. Problemstellung.- 7.2. Testfunktionen.- 7.3. Verallgemeinerte Funktionen.- 7.4. Die Diracsche Deltafunktion.- 7.5. Die Derivierte einer verallgemeinerten Funktion.- 7.6. Produkte von verallgemeinerten Funktionen. Das Funktional ?(g(x)).- 7.7. Die uneigentliche Funktion ?(1/r).- 7.8. Ergänzungen und Bemerkungen.- 7.9. Übungsbeispiele zu Kap. 7.- 8. Die Methode der Greenschen Funktionen für partielle Differentialgleichungen.- 8.1. Die klassische Lösung der Poissongleichung.- 8.2. Greensche Funktionen und die Deltafunktion.- 8.3. Die Greensche Funktion der Poissongleichung.- 8.3.1. Der eindimensionale Fall.- 8.3.2. Der dreidimensionale Fall mit natürlichen Randbedingungen.- 8.4. Die Greensche Funktion der Wärmeleitung (Diffusion).- 8.4.1. Die Wärmeleitung im unendlich langen Stab.- 8.4.2. Anfangs- und Randbedingungen der homogenen Wärmeleitungsgleichung.- 8.4.3. Die Wärmeleitung im Raum.- 8.5. Die Greenschen Funktionen der Wellengleichung und ihrer Verallgemeinerungen.- 8.5.1. Allgemeine Randbedingungen.- 8.5.2. Greensche Funktionen im unendlichen Raum.- 8.6. Übungsbeispiele zu Kap. 8.- A. Funktionentheorie.- B. Die Gammafunktion.- Literatur.- Sachwortverzeichnis.
£53.99
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 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 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-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 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 Spektrum Das Zwillingsparadoxon
Book Synopsis
£11.77
Springer Fachmedien Wiesbaden Grundkurs Theoretische Physik 5/2:
Book SynopsisDer beliebte Grundkurs Theoretische Physik deckt in sieben Bänden alle für das Bachelor-/Master- oder Diplomstudium maßgeblichen Gebiete ab. Jeder Band vermittelt gut durchdacht das im jeweiligen Semester nötige theoretisch-physikalische Rüstzeug. Zahlreiche Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffes. Der zweite Teil des fünften Bandes befasst sich mit Anwendungen und mit dem Ausbau der im ersten Teil entwickelten Konzepte der Quantenmechanik.Die vorliegende neue Auflage enthält einige neue Aufgaben, wurde grundlegend überarbeitet und durch einige Zusatzkapitel zur Streutheorie ergänzt. Sie ermöglicht durch die zweifarbige Darstellung einen sehr übersichtlichen und schnellen Zugriff auf den Lehrstoff.Table of ContentsQuantentheorie des Drehimpulses.- Zentralpotential.- Näherungsmethoden.- Mehr-Teilchen-Systeme.- Streutheorie.- Lösungen der Übungsaufgaben.
£47.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Supermathematics and its Applications in Statistical Physics: Grassmann Variables and the Method of Supersymmetry
Book SynopsisThis text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.Trade Review“This volume of Lecture Notes in Physics presents in three parts the topics of Grassmann algebra and its applications and the subject of supermathematics, where commuting and anticommuting variables are treated on equal footing, and its applications. … it may be of interest to those already in the field who want to expand their knowledge in both the underlying mathematics and its applications in physics.” (Moorad Alexanian, Mathematical Reviews, January, 2017)“Each chapter contains a set of illustrating problems supplied with answers in the book's end. Thus, this monograph can be used for practical teaching as well.” (Eugene Postnikov, zbMATH 1345.81003, 2016)Table of ContentsPart I Grassmann Variables and Applications.- Part II Supermathematics.- Part III Supersymmetry in Statistical Physics.- Summary and Additional Remarks.- References.- Solutions.- Index.
£47.69
Springer Fachmedien Wiesbaden Einführung in die Theoretische Physik: Klassische
Book SynopsisDieses Lehrbuch bietet Studierenden der ersten Semester eine Einführung in die Theoretische Physik sowie die dazu erforderlichen mathematischen Werkzeuge. Parallel zu den Inhalten der Klassischen Mechanik lernen Sie die nötige Mathematik gleich mit – und auch die Denkweise in der Theoretischen Physik kennen. Unter sorgfältiger Berücksichtigung des Wissensstands von Studienanfängern wird eine ausführliche, schrittweise Darstellung von allen Herleitungen und Beispielen geboten. Dabei werden Ihnen nicht nur die analytischen Lösungsverfahren gezeigt, sondern Sie erhalten auch einen Einblick in die große Bedeutung von computergestützten, numerischen Verfahren. Das Buch beginnt mit den Leitbegriffen des Zustands und der Bewegungsgleichung, worauf aufbauend die Struktur der Newton‘schen Mechanik in leicht nachvollziehbarer Art und Weise vermittelt wird. Als dazugehörige mathematische Themen werden komplexe Zahlen, Vektoren und Matrizen, Taylor-Reihen, gewöhnliche Differenzialgleichungen, Fourier-Reihen, partielle Ableitungen und Elemente der Vektoranalysis behandelt. Ebenso finden Sie in diesem Buch eine Untersuchung elementarer Erhaltungssätze als auch deren Anwendung auf physikalische Fragestellungen wie z.B. die Begründung der Kepler‘schen Gesetze.Table of ContentsVorwort.- 1 Grundkonzepte.- 2 Beschreibung der Bewegung von Massenpunkten.- 3 Dynamische Gesetze für einen Massenpunkt.- 4 Gewöhnliche Differenzialgleichungen.- 5 Fourier-Reihen.- 6 Nichtlineare Dynamik.- 7 Systeme mit mehr als einem Teilchen.- 8 Partielle Ableitungen.- 9 Energie.- 10 Zweiteilchenproblem mit Gravitationskraft.- 11 Drehbewegungen.- 12 Spezielle Relativitätstheorie - 13 Anhänge: A Computerprogramm zu Kap. 1.- B Computerprogramm zu Kap. 6.- Index.
£26.59
Springer Fachmedien Wiesbaden Komplexe Strukturen: Entropie und Information
Book SynopsisDie Erforschung komplexer Strukturen ist gegenwärtig eines der interessantesten wissenschaftlichen Themen. Dieses Buch behandelt Möglichkeiten der Beschreibung und quantitativen Charakterisierung komplexer Strukturen mit Hilfe verschiedener Entropie- und Informationsmaße. Nach einer allgemein verständlichen Einführung der Grundbegriffe werden die für eine quantitative Analyse erforderlichen Konzepte ausführlich behandelt und an zahlreichen Beispielen, wie Zeitreihen, Biosequenzen, literarischen Texten und Musikstücken, veranschaulicht.Table of ContentsKomplexität und Entropie - Selbstorganisation und Information - Informationstheoretische Maße - Dynamisch generierte Strukturen - Entropie und Komplexität natürlicher Sequenzen - Quantitative Ästhetik
£44.99
Springer Verlag Note di fisica statistica
Book SynopsisIl testo si configura come un' introduzione alla fisica statistica rivolto in primo luogo a quei corsi di studio in ingegneria che più hanno a che fare con le proprietà fisiche dei materiali, ed ha lo scopo di fornire le basi microscopiche del comportamento termodinamico di cui si fa uso sia in molti corsi tradizionali, quali quelli di termofluidica d'interesse per l'ingegneria chimica e nucleare, che in corsi rivolti ad applicazioni avanzate nella scienza dei materiali e nelle nanotecnologie. Particolare attenzione viene quindi dedicata all'impiego di metodi di fisica statistica nella scienza dei materiali, approfondendo tematiche relative alle vibrazioni nei solidi, ai processi di nucleazione liquido/vapore, alla struttura dello stato fluido e vetroso, ai plasmi, ai materiali magnetici, al gas di Fermi e alla superfluidità. Per il suo carattere generale, e per l'accento posto sui fondamenti della meccanica quantistica, il volume si presta comunque a costituire anche un testo introduttivo alla meccanica statistica per studenti dei corsi di laurea in fisica.Trade ReviewFrom the reviews:“The book covers the main typical arguments of a course on statistical physics and thermodynamics in the Italian university system. … the author intends to transmit to the readers: the subject of statistical physics is not only useful, but is also far to be boring and can reveal an intrinsic beauty. Also, the style of writing the different chapters reveals the intention of the author to give a pleasant environment for the study of the subject.” (Francesco Salvarani, Zentralblatt MATH, Vol. 1241, 2012)
£49.49
Birkhauser Verlag AG Numerical methods for atomic quantum gases
Book SynopsisThe achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. High purity and easy optical access make them ideal candidates to investigate fundamental issues on interacting quantum systems. This review presents some theoretical issues which have been addressed in this area and the numerical techniques which have been developed and used to describe them, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties. The attention given in this article to methods beyond standard mean-field approaches should make it a useful reference point for future advances in these areas.
£17.09
Birkhauser Verlag AG Highlights in the quantum theory of condensed
Book SynopsisThe birth of condensed matter physics in Italy is linked to a small number of very distinguished scientists. Mario Tosi, Professor of Physics of Matter at the Scuola Normale Superiore, is unquestionably among the leading figures, a true founder of the theoretical activity in the country and a true catalyst of novel research directions internationally. This volume collects the proceedings of a symposium held at Scuola Normale Superiore di Pisa, designed to show Mario Tosi's broad, deep influence in very diverse areas of the quantum theory of condensed matter. The topics covered in the volume represent the breadth of his interests and the highlights in the quantum theory of condensed matter: liquids, electronic states in complex structures, quantum degenerate gases, many-body physics.
£18.04
Birkhauser Verlag AG Symmetry in physics
Book SynopsisThese notes contain lectures on the theory of group representations and its applications to the physics of atoms, molecules and crystals, given at Purdue University, Scuola Normale Superiore (Pisa, Italy) and Universidad Técnica Federico Santa Maria (Valparaiso, Chile) on and off over a period of over 25 years. The topics selected reflect my special interests and their scope is limited by the time available to the students. The style is somewhat concise and will require careful attention on the part of the reader.
£11.99
Birkhauser Verlag AG An introduction to computational physics: Part I:
Book SynopsisThese volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. Grid methods are the tool of the trade for the solution of ordinary and partial differential equations and consequently they represent a “must” for anyone dealing with computational science. With grid methods, a major distinction is made between methods which do not require matrix algebra and those which do.
£11.99
Birkhauser Verlag AG An introduction to computational physics: Part
Book SynopsisThese volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. The second part deals with various types of particle methods, both deterministic and stochastic, used in modern applications of computer simulations in physics and related disciplines.
£11.99
Birkhauser Verlag AG Lectures on nonlinear physics
Book SynopsisThe main goal of these lectures is to get students acquainted with a glossary of nonlinear physics. I try to present the material of the lectures (delivered at SNS Pisa in April -- June 1999) in such a way that the students do not need to use additional literature during the first reading. The lectures focus on the following arguments: discussion of nonlinear problems in classical physics; the use of the multiple time scale expansion method to solve problems of nonlinear oscillations; description of nonlinear wave steepening and shock wave formation using the Lagrange variables; solution of nonlinear elliptic equations considering the Liouville equation; soliton solutions of the Korteweg de Vries, Sine-Gordon and Nonlinear Schrödinger equations; the use of the Backlund transformation; self-similarity of nonlinear systems.
£11.99
Birkhauser Verlag AG Ground state properties and excitation spectrum
Book SynopsisElectron gas theory is one of the broadest fields in theoretical condensed matter physics, and even its most elementary application to the study of collective excitations and screening in the simpe metals poses interesting questions. Recent Electron Energy Loss and Inelastic X-Ray Scattering experiments have shown that traditional electron gas theories are unable to account for the measured plasmon dispersion relation. While it has become clear that neither correlation nor band structure alone can explain those results, the recently developed Time Dependent Density Functional Theory provides a general framework which can account for both.
£14.98
Birkhauser Verlag AG Quantum Gases in Quasi-One-Dimensional Arrays
Book SynopsisThe experimental achievement of Bose-Einstein condensation (1995) and of Fermi degeneracy (1999) in ultra-cold, dilute gases has opened a new field in atomic physics and condensed matter physics. This thesis presents an overview of theoretical and experimental facts on ultra-cold atomic gases. A Green's function scheme is examined, and the book also applies a novel spin-density-functional approach to the study of Fermi gases inside one-dimensional optical lattices.Table of ContentsPreface.- 1. Reviews on Ultra-cold quantum gases.- 2. Theory of matter transport in quasi-1D arrays.- 3. Density-functional theory of 1D Fermi gases.- 4. Ultra-cold attractive fermions in 1D optical lattices.
£14.99
Birkhauser Verlag AG Asymptotics in Dynamics, Geometry and PDEs;
Book SynopsisThese are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
£26.99
Birkhauser Verlag AG Resurgence, Physics and Numbers
Book SynopsisThis book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years – a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues. Table of ContentsAsymptotics, ambiguities and resurgence.- Nonlinear eigenvalue problems.- Feynman diagrams and their algebraic lattices.- Invariants of identity-tangent diffeomorphisms expanded as series of multitangents and multizetas.- The resurgent approach to topological string theory.- WKB and resurgence in the Mathieu equation.- Renormalised conical zeta values.- Combinatorics of Poincaré's and Schröder's equations.
£21.84
Springer Unbounded Self-adjoint Operators on Hilbert Space
Book SynopsisThe book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extensionTrade ReviewFrom the reviews:“The book is devoted to the exposition of the theory of unbounded operators in the Hilbert space. … book starts with a standard introduction to the theory of closed and closable operators, with an explanation of the important difference between self-adjoint and symmetric operators. … Among the advantages of the book is the inclusion of a nice and voluminous selection of exercises. … the book can be used for teaching a graduate course in spectral theory to students in analysis and to physicists … .” (G. V. Rozenblum, Mathematical Reviews, January, 2013)“I recommend the book as a reference for readers interested in the general theory of unbounded self-adjoint operators in Hilbert space. It is a valuable reference for numerous topics, including closed and adjoint operators, the general spectral theorem for self-adjoint operators, groups and semigroups of operators, semibounded and sectorial forms and their associated operators, and self-adjoint extensions of symmetric operators. … A special feature of the book is the inclusion of numerous examples based on multiplication operators and first and second order differential operators.” (Anton Zettl, SIAM Review, Vol. 55 (3), 2013)“The book can be used for teaching a graduate course in spectral theory to students and is also suitable for self-study. The book consists of six parts, each of which is subdivided into several chapters, each chapter ending with a section containing exercises. … The book concludes with appendices devoted to basic topics in analysis and the theory of bounded operators.” (Michael Perelmuter, Zentralblatt MATH, Vol. 1257, 2013)Table of ContentsI Basics onClosed Operators.- 1 Closed Operators and Adjoint Operators.- 2 Spectrum of Closed Operators.- 3 Some Classes of Unbounded Operators.- II Spectral Theory.- 4 Spectral Measures and Spectral Integrals.- 5 Spectral Decomposition of Selfadjoint and Normal Operators.- III Special Topics.- 6 One-Parameter Groups and Semigroups of Operators.- 7 Miscellaneous.- IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators.- 8 Perturbations of Selfadjoint Operators.- 9 Trace Class Perturbations of Spectra of Selfadjoint Operators.- V Forms and Operators.- 10 Semibounded Forms and Selfadjoint Operators.- 11 Sectorial Forms and m-Sectorial Operators.- 12 Discrete Spectrum of Selfadjoint Operators.- VI Selfadjoint Extention Theory of Symmetric Operators.- 13 Selfajoint Extensions: Cayley Transform and Krein Transform.- 14 Selfadjoint Extensions: Boundary Triplets.- 15 Sturm-Liouville Operators.- One-Dimensional Moment Problem.
£54.99
Springer Verlag, Singapore The Special Theory of Relativity: A Mathematical Approach
Book SynopsisThis textbook expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics, and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the text discusses the relativistic effect on photons. A new chapter on electromagnetic waves as well as several new problems and examples have been included in the second edition of the book. Using the mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 15 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the text provides numerous relevant worked-out examples in every chapter. The mathematical approach of the text helps students in their independent study and motivates them to research the topic further.Table of ContentsPre-Relativity and Galilean Transformations.- Michelson-Morley Experiment and Velocity of Light.- Lorentz Transformations.- Mathematical Properties of Lorentz Transformations.- More mathematical Properties of Lorentz Transformations.- Geometrical Interpretation of spacetime.- Relativistic Velocity and Acceleration.- Four Dimensional World.- Mass in Relativity.- Relativistic Dynamics.- Photon in Relativity.- Relativistic Lagrangian and Hamiltonian.- Electrodynamics in Relativity.- Electromagnetic waves.- Relativistic Mechanics of Continua.
£49.49
Springer Verlag, Singapore Synergies in Analysis, Discrete Mathematics, Soft
Book SynopsisThis book contains select papers on mathematical analysis and modeling, discrete mathematics, fuzzy sets, and soft computing. All the papers were presented at the international conference on FIM28-SCMSPS20 virtually held at Sri Sivasubramaniya Nadar (SSN) College of Engineering, Chennai, India, and Stella Maris College (Autonomous), Chennai, from November 23–27, 2020. The conference was jointly held with the support of the Forum for Interdisciplinary Mathematics. Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters).Table of ContentsPART I ANALYSIS AND MODELLINGThe Second- and Third-order Hermitian Toeplitz Determinants for Some Subclasses of Analytic Functions Associated with Exponential Function,P.Gurusamy, R. Jayasankar and S. SivasubramanianSome Results on a Starlike Class with Respect to $(j, m) $-symmetric FunctionsK. Renuka Devi, S. Sivasubramanian, Hamid Shamsan and S. LathaExperimental Evaluation of Four Intermediate Filters to Improve the Motion Field EstimationVanel Lazcano and Claudio Isa-MohorOn the $s^{th}$ Derivative of a PolynomialBarchand Chanam and Kshetrimayum KrishnadasOn the Problem of Pricing a Double Barrier Option in a Modified Black–Scholes Environment G. Venkiteswaran and S. UdayabaskaranCaputo Sequential Fractional Differential Equations with ApplicationsAghalaya S. Vatsala and Govinda PageniPART II DISCRETE MATHEMATICS AND APPLICATIONSHerscovici’s Conjecture on Product of Some Complete Bipartite GraphsA. Lourdusamy and S. Saratha NellainayakiOn Fault-Tolerant Metric Dimension of Heptagonal Circular Ladder and Its Related GraphsSunny Kumar Sharma and Vijay Kumar BhatBKS Fuzzy Inference Employing h-ImplicationsSayantan Mandal and Balasubramaniam Jayaram Note on Distributivity of Different String Operations over Language SetsUjjwal Kumar Mishra, Kalpana Mahalingam and Rama RaghavanA Generalization of Chi-binding FunctionsM. A. Shalu and T. P. SandhyaA Short Proof of Ore’s f-factor Theorem using FlowsSriraman Sridharan and Patrick VilamajoPART III FUZZY SETS AND SOFT COMPUTINGA Decision-making Problem Involving Soft Fuzzy Number Valued Information System: Energy Efficient Light Emitting Diode BlubsFelbin C. Kennedy, Masilla Moses Kennedy, Arul Roselet Meryline S. andJayachandiran M.Role of Single-valued Linear Octagonal Neutrosophic Numbers in Multi-attribute Decision-making ProblemsSubasri S., Arul Roselet Meryline S. and Felbin C. Kennedy
£98.99
Springer-Verlag GmbH Proceedings of the 2nd International Conference on Sustainability and Emerging Technologies for Smart Manufacturing
£246.39
Springer Transverse Instability of Solitary Waves
Book SynopsisChapter 1 Introduction.- Chapter 2 Literature Review.- Chapter 3 Multisymplectic Wave Equations and Dirac Operators.- Chapter 4 Solitary Wave Solutions and Their Properties.- Chapter 5 Linearisation about Solitary Waves.- Chapter 6 Spectral Stability and the Evans Function.- Chapter 7 Derivatives of the Evans Function.- Chapter 8 Summary of Hypotheses Used.- Chapter 9 Example: Nonlinear Wave Equation in 2 + 1.- Chapter 10 Concluding Remarks.
£107.99
Springer Fractional Derivatives for Physicists and
Book Synopsis
£134.99
