Mathematical / Computational / Theoretical physics Books
Springer London Ltd General Relativity
Book SynopsisBased on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.Trade ReviewFrom the reviews:“This book introduces General Relativity at students level, especially intended for final year mathematics students. Different from other books with the same title, it really goes into the geometric details and tries to explain the given formulae … . The appendices present exercises and hints to their solutions.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014)"I have the opportunity to comment on General Relativity … . I am happy to recommend … for an advanced undergraduate course on relativity or for self-study. … marvelous faithfulness to historical developments … characterizes the entire treatment. … In fact, the whole book is distinguished by this high quality of exposition. … It’s a fine book, beautifully written and clear, and I highly recommend it." (Michael Berg, MathDL, January, 2007)MAA Reviews:In December, 2003 I had the pleasure of reviewing the admirable book Special Relativity, by N.M.J. Woodhouse, and now I have the opportunity to comment on General Relativity by the same author. I am happy to recommend not just this sequel, but the indicated pair, for an advanced undergraduate course on relativity or for self-study.One particularly noteworthy feature of General Relativity is that woodhouse seeks to present the subject neither as a branch of differential geometry nor as the kind of physics mathematicians like me find unapproachable (and I'm afraid this doesn't particularly narrow the field). When just a rookie I dabbled in relativity largely from popularizations and biographical writings, and when I tried to learn some real general relativity in graduate school - for cultural reasons, I guess - it simply didn't take. But my interest in the subject, both specially and generally, has never flagged and Woodhouse’s books are tailor-made for even my lingering ambitions. In other words, for any slacker who feels he should have learned this beautiful material in his mathematical youth, but didn’t, and is now secretly (or not so secretly) desirous of doing it right, this is the book, or, more correctly, these are the books to read. Furthermore, as I already hinted, as far as teaching courses on these important subjects is concerned, obviously these books fit that bill very well too, given Woodhouse’s specific pedagogical intent.When it comes to the specific style and presentation of general relativity chosen by Woodhouse, marvellous faithfulness to historical developments, in particular Einstein’s own writings, characterizes the entire treatment. On p.7, already, the weak and strong equivalence principles are presented and analysed in a succinct and historically rooted fashion. The former, going back to Galileo’s pendulums (Woodhouse correctly says "pendula," of course) and famously connected with Eötvös’ experiment, entails that inertial mass and gravitational mass are the same; and the latter says that there are no obvservable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these observable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these incomparable axioms underlying Einstein’s revolution is a gem of exposition, covering the historical sweep of the attendant experiments (he even mentions a planned space experiment, "STEP," which will test the latter principle to within one part in 1018) and conveying what is to come as a result of these stipulations. Finally, I want to draw special attention to pp.23-27, where Woodhouse does a phenomenally good job of explicating the subject of tensors in Minkowski space, a subject which has always been a bit unsettling to me who was raised to visit tensor products in their homological algebraic home and I cannot resist mentioning Problem 1.5 on p.13, dealing with "Einstein’s birthday present."It’s a fine book, beautifully written and clear, and I highly recommend it. [Reviewed by Michael Berg, 20.1.2007]"Woodhouse … lets the physical intuition behind relativity inform every step of its logical development, making his treatment as digestible as any in print. He does introduce ab ovo what differential geometry he needs, and he takes the whole theory far enough to develop general relativity’s most exciting predictions, black holes and gravity waves, all in less than half the number of pages one might expect. Summing Up: Highly recommended. Upper-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. 44 (11), July, 2007)"The book is an outgrowth of a lecture course given over many years by the author and his colleagues to final-year applied mathematicians at the Mathematical Institute in Oxford, UK. The book is well-written and easy to follow because the author constructs the necessary apparatus layer-by-layer, from the bottom up, carefully motivating and justifying every new concept. Exercises are given at the end of every chapter … and numerous examples appear throughout the text. … its expository style is very appealing." (David A. Burton, General Relativity and Gravitation, Vol. 39, 2007)Table of ContentsNewtonian Gravity.- Inertial Coordinates and Tensors.- Energy-Momentum Tensors.- Curved Space—Time.- Tensor Calculus.- Einstein’s Equation.- Spherical Symmetry.- Orbits in the Schwarzschild Space—Time.- Black Holes.- Rotating Bodies.- Gravitational Waves.- Redshift and Horizons.
£32.99
Springer London Ltd Introduction to Analytical Dynamics
Book SynopsisFirst published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding. Trade ReviewFrom the reviews of the second edition:“It is designed to teach analytical mechanics to second and third year undergraduates in the UK, and probably to third or fourth year undergraduates in the US. … This book offers a very attractive traditional introduction to the subject. … the author is well tuned to the difficulties even strong students encounter. … discusses the relevance of classical mechanics in modern physics, especially to relativity and quantum mechanics. This is a fine textbook. It would be a pleasure to teach or to learn from it.” (William J. Satzer, The Mathematical Association of America, March, 2010)Table of ContentsFrames of Reference.- One Degree of Freedom.- Lagrangian Mechanics.- Noether#x2019;s Theorem.- Rigid Bodies.- Oscillations.- Hamiltonian Mechanics.- Geometry of Classical Mechanics.- Epilogue: Relativity and Quantum Theory.
£24.95
Springer London Ltd Special Relativity
Book SynopsisThis book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.Trade ReviewFrom the reviews: N.M.J. Woodhouse's comparatively short Special Relativity is a pleasure to read and therefore qualifies right off as a good source to use for learning about special relativity on your own. A lot of very nice material is touched on in its pages, presented in natural sequence consonant with history, and is not improperly belabored. It's also rather informal in style. One gets the sense of breezing along pretty fast while, in actuality, a lot of material is being dealt with... the selection of topics in the book is very nice indeed , and is historically sound and will therefore reward the reader with an element of culture to boot: he'll learn some history of modern physics... I wish this book had been around when I was a student. MAA Online ...an exciting and challenging book with which to introduce a modern mathematics student in a single course to the great ideas of Maxwell's theory and special relativity. The Australian Mathematical Society Gazette "There are many books on special relativity for undergraduates, and this one is notable in that it is specifically addressed to mathematicians. … this book will be found illuminating by students of mathematics … ." (Dr. P. E. Hodgson, Contemporary Physics, Vol. 45 (5), 2004) "This book is … aimed squarely at the undergraduate mathematician ... . The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. … There are lots of examples and nicely graded exercises throughout the text, and each chapter ends with a usefully annotated bibliography. The author’s friendly style, and the fact the material has been developed from taught courses make the book ideal for self-study … ." (Peter Macgregor, The Mathematical Gazette, Vol. 88 (512), 2004) "Meant as a resource for advanced undergraduate students, this book approaches special relativity theory from a mathematical perspective … . It is best used for mathematics majors … . the text is clear, well written, and has an adequate bibliography. Summing Up: Recommended. Upper-division undergraduates." (A. Spero, CHOICE, December, 2003) "This presentation is very elegant … . The book contains a large number of examples. Each chapter is followed by exercises, ranging from the rather simple to the more involved. This book is certainly a good introduction to special relativity, understandable for second-year students. But it is also interesting for readers searching for a concise and precise presentation of special relativity within the tensor formalism." (Claude Semay, Physcalia, Vol. 25 (4), 2003)Table of Contents1. Relativity in Classical Mechanics.- 1.1 Frames of Reference.- 1.2 Relativity.- 1.3 Frames of Reference.- 1.4 Newton’s Laws.- 1.5 Galilean Transformations.- 1.6 Mass, Energy, and Momentum.- 1.7 Space-time.- 1.8 *Galilean Symmetries.- 1.9 Historical Note.- 2. Maxwell’s Theory.- 2.1 Introduction.- 2.2 The Unification of Electricity and Magnetism.- 2.3 Charges, Fields, and the Lorentz Force Law.- 2.4 Stationary Distributions of Charge.- 2.5 The Divergence of the Magnetic Field.- 2.6 Inconsistency with Galilean Relativity.- 2.7 The Limits of Galilean Invariance.- 2.8 Faraday’s Law of Induction.- 2.9 The Field of Charges in Uniform Motion.- 2.10 Maxwell’s Equations.- 2.11 The Continuity Equation.- 2.12 Conservation of Charge.- 2.13 Historical Note.- 3. The Propagation of Light.- 3.1 The Displacement Current.- 3.2 The Source-free Equations.- 3.3 The Wave Equation.- 3.4 Monochromatic Plane Waves.- 3.5 Polarization.- 3.6 Potentials.- 3.7 Gauge Transformations.- 3.8 Photons.- 3.9 Relativity and the Propagation of Light.- 3.10 The Michelson-Morley Experiment.- 4. Einstein’s Special Theory of Relativity.- 4.1 Lorentz’s Contraction.- 4.2 Operational Definitions of Distance and Time.- 4.3 The Relativity of Simultaneity.- 4.4 Bondi’s fc-Factor.- 4.5 Time Dilation.- 4.6 The Two-dimensional Lorentz Transformation.- 4.7 Transformation of Velocity.- 4.8 The Lorentz Contraction.- 4.9 Composition of Lorentz Transformations.- 4.10 Rapidity.- 4.11 *The Lorentz and Poincaré Groups.- 5. Lorentz Transformations in Four Dimensions.- 5.1 Coordinates in Four Dimensions.- 5.2 Four-dimensional Coordinate Transformations.- 5.3 The Lorentz Transformation in Four Dimensions.- 5.4 The Standard Lorentz Transformation.- 5.5 The General Lorentz Transformation.- 5.6 Euclidean Space and Minkowski Space.- 5.7 Four-vectors.- 5.8 Temporal and Spatial Parts.- 5.9 The Inner Product.- 5.10 Classification of Four-vectors.- 5.11 Causal Structure of Minkowski Space.- 5.12 Invariant Operators.- 5.13 The Frequency Four-vector.- 5.14 * Affine Spaces and Covectors.- 6. Relative Motion.- 6.1 Transformations Between Frames.- 6.2 Proper Time.- 6.3 Four-velocity.- 6.4 Four-acceleration.- 6.5 Constant Acceleration.- 6.6 Continuous Distributions.- 6.7 *Rigid Body Motion.- 6.8 Visual Observation.- 7. Relativistic Collisions.- 7.1 The Operational Definition of Mass.- 7.2 Conservation of Four-momentum.- 7.3 Equivalence of Mass and Energy.- 8. Relativistic Electrodynamics.- 8.1 Lorentz Transformations of E and B.- 8.2 The Four-Current and the Four-potential.- 8.3 Transformations of E and B.- 8.4 Linearly Polarized Plane Waves.- 8.5 Electromagnetic Energy.- 8.6 The Four-momentum of a Photon.- 8.7 *Advanced and Retarded Solutions.- 9. *Tensors and Isomet ries.- 9.1 Affine Space.- 9.2 The Lorentz Group.- 9.3 Tensors.- 9.4 The Tensor Product.- 9.5 Tensors in Minkowski Space.- 9.6 Tensor Components.- 9.7 Examples of Tensors.- 9.8 One-parameter Subgroups.- 9.9 Isometries.- 9.10 The Riemann Sphere and Spinors.- Notes on Exercises.- Vector Calculus.
£29.99
Fisher Sharp Shooters, LLC Straight Shooter: A game-changing new approach to basketball shooting
£15.95
Santa Fe Institute of Science Complexity, Entropy, and the Physics of Information (Volume I)
£20.99
Santa Fe Institute of Science Complexity, Entropy & the Physics of Information (Volume II)
£20.99
Createspace Independent Publishing Platform An Introduction to Computer Simulation Methods: Applications To Physical Systems
£38.04
Springer Nature Switzerland AG Tensor Network Contractions: Methods and Applications to Quantum Many-Body Systems
Book SynopsisTensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics. Trade Review“This book is particularly suitable for students and researchers who are new in this field. It is a timely book that provides a concise introduction of the important topics in this brand-new field with promising prospects. Furthermore, the book provides an up-to-date brief review, which is well suited as a reference for experience researchers.” (Hong-Hao Tu, zbMATH 1442.81003, 2020)Table of ContentsIntroduction.- Tensor Network: Basic Definitions and Properties.- Two-Dimensional Tensor Networks and Contraction Algorithms.- Tensor Network Approaches for Higher-Dimensional Quantum Lattice Models.- Tensor Network Contraction and Multi-Linear Algebra.- Quantum Entanglement Simulation Inspired by Tensor Network.- Summary.
£44.99
Springer Nature Switzerland AG Applied Holography: A Practical Mini-Course
Book SynopsisThis primer is a collection of notes based on lectures that were originally given at IIT Madras (India) and at IFT Madrid (Spain). It is a concise and pragmatic course on applied holography focusing on the basic analytic and numerical techniques involved. The presented lectures are not intended to provide all the fundamental theoretical background, which can be found in the available literature, but they concentrate on concrete applications of AdS/CFT to hydrodynamics, quantum chromodynamics and condensed matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details for the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during the author’s research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by him/herself more advanced techniques and to produce independent and novel research in the field.Table of ContentsA Strings-less introduction to AdS-CFT.- A Practical Understanding of the Dictionary.- The first big success: η/s and Hydrodynamics.- Holographic Transport via analytic and numerical techniques.
£54.99
Springer Nature Switzerland AG Entropy and the Tao of Counting: A Brief
Book SynopsisThis book provides a complete and accurate atomic level statistical mechanical explanation of entropy and the second law of thermodynamics. It assumes only a basic knowledge of mechanics and requires no knowledge of calculus. The treatment uses primarily geometric arguments and college level algebra. Quantitative examples are given at each stage to buttress physical understanding. This text is of benefit to undergraduate and graduate students, as well as educators and researchers in the physical sciences (whether or not they have taken a thermodynamics course) who want to understand or teach the atomic/molecular origins of entropy and the second law. It is particularly aimed at those who, due to insufficient mathematical background or because of their area of study, are not going to take a traditional statistical mechanics course.Table of Contents
£44.99
Springer Nature Switzerland AG An Introductory Path to Quantum Theory: Using
Book SynopsisSince the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.Trade Review“The target audience is ‘advanced undergraduate mathematics students who had no or only very little prior knowledge of physics’. It would indeed be a rare variety of mathematics advanced undergraduates who would fit this bill. … an interesting supplement for students with a mathematical bent.” (Amitava Raychaudhuri, zbMATH 1458.81002, 2021)Table of ContentsIntroduction to this Path.- Viewpoint.- Neither Particle nor Wave.- Schrödinger's Equation.- Operators and Canonical Quantization.- The Harmonic Oscillator.- Interpreting: Mathematics.- Interpreting: Physics.- The Language of Hilbert Space.- Interpreting: Measurement.- The Hydrogen Atom.- Angular Momentum.- The Rotation Group SO(3).- Spin and SU(2).- Bosons and Fermions.- Classical and Quantum Probability.- The Heisenberg Picture.- Uncertainty (Optional).- Speaking of Quantum Theory (Optional).- Complementarity (Optional).- Axioms (Optional).- And Gravity?.- Measure Theory: A Crash Course.
£49.99
Springer Nature Switzerland AG Statistical Field Theory for Neural Networks
Book SynopsisThis book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.Table of ContentsI. IntroductionII. Probabilities, moments, cumulantsA. Probabilities, observables, and momentsB. Transformation of random variablesC. CumulantsD. Connection between moments and cumulantsIII. Gaussian distribution and Wick’s theoremA. Gaussian distributionB. Moment and cumulant generating function of a GaussianC. Wick’s theoremD. Graphical representation: Feynman diagramsE. Appendix: Self-adjoint operatorsF. Appendix: Normalization of a GaussianIV. Perturbation expansionA. General caseB. Special case of a Gaussian solvable theoryC. Example: Example: “phi^3 + phi^4” theoryD. External sourcesE. Cancellation of vacuum diagramsF. Equivalence of graphical rules for n-point correlation and n-th momentG. Example: “phi^3 + phi^4” theoryV. Linked cluster theoremA. General proof of the linked cluster theoremB. Dependence on j - external sources - two complimentary viewsC. Example: Connected diagrams of the “phi^3 + phi^4” theoryVI. Functional preliminariesA. Functional derivative1. Product rule2. Chain rule3. Special case of the chain rule: Fourier transformB. Functional Taylor seriesVII. Functional formulation of stochastic differential equationsA. Onsager-Machlup path integral*B. Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) path integralC. Moment generating functionalD. Response function in the MSRDJ formalismVIII. Ornstein-Uhlenbeck process: The free Gaussian theoryA. DefinitionB. Propagators in time domainC. Propagators in Fourier domainIX. Perturbation theory for stochastic differential equationsA. Vanishing moments of response fieldsB. Vanishing response loopsC. Feynman rules for SDEs in time domain and frequency domainD. Diagrams with more than a single external legE. Appendix: Unitary Fourier transformX. Dynamic mean-field theory for random networksA. Definition of the model and generating functionalB. Property of self-averagingC. Average over the quenched disorderD. Stationary statistics: Self-consistent autocorrelation of as motion of a particle in a potentialE. Transition to chaosF. Assessing chaos by a pair of identical systemsG. Schrödinger equation for the maximum Lyapunov exponentH. Condition for transition to chaosXI. Vertex generating functionA. Motivating example for the expansion around a non-vanishing mean valueB. Legendre transform and definition of the vertex generating function GammaC. Perturbation expansion of GammaD. Generalized one-line irreducibilityE. ExampleF. Vertex functions in the Gaussian caseG. Example: Vertex functions of the “phi^3 + phi^4”-theoryH. Appendix: Explicit cancellation until second orderI. Appendix: Convexity of WJ. Appendix: Legendre transform of a GaussianXII. Application: TAP approximationInverse problemXIII. Expansion of cumulants into tree diagrams of vertex functionsA. Self-energy or mass operator SigmaXIV. Loopwise expansion of the effective action - Tree levelA. Counting the number of loopsB. Loopwise expansion of the effective action - Higher numbers of loopsC. Example: phi^3 + phi^4-theoryD. Appendix: Equivalence of loopwise expansion and infinite resummationE. Appendix: Interpretation of Gamma as effective actionF. Loopwise expansion of self-consistency equationXV. Loopwise expansion in the MSRDJ formalismA. Intuitive approachB. Loopwise corrections to the effective equation of motionC. Corrections to the self-energy and self-consistencyD. Self-energy correction to the full propagatorE. Self-consistent one-loopF. Appendix: Solution by Fokker-Planck equationXVI. NomenclatureAcknowledgmentsReferences
£59.99
Springer Nature Switzerland AG An Invitation to Mathematical Physics and Its History
Book SynopsisThis state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.Table of ContentsIntroduction.- Number Systems.- Algebraic Equations.- Scalar Calculus.- Vector Calculus.
£54.99
Springer Nature Switzerland AG The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics: A Primer for Advanced Undergraduates
Book SynopsisThe field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.Table of ContentsWeierstrass Elliptic Function.- Weierstrass Quasi-periodic Functions.- Real Solutions of Weierstrass Equation.- Applications in Classical Mechanics.- Applications in Quantum Mechanics.- Epilogue and Projects for the Advanced Reader.
£54.99
Springer Nature Switzerland AG Mathematical Concepts of Quantum Mechanics
Book SynopsisThe book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline.Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content.It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.Table of Contents1 Physical Background.- 2 Dynamics.- 3 Observables.- 4 Quantization.- 5 Uncertainty Principle and Stability of Atoms and Molecules.- 6 Spectrum and Dynamics.- 7 Special Cases.- 8 Bound States and Variational Principle.- 9 Scattering States.- Existence of Atoms and Molecules.- 11 Perturbation Theory: Feshbach-Schur Method.- 12 Born-Oppenheimer Approximation and Adiabatic Dynamics.- 13 General Theory of Many-particle Systems.- 14 Self-consistent Approximations.- 15 The Feynman Path Integral.- 16 Semi-classical Analysis.- 17 Resonances.- 18 Quantum Statistics.- 19 Open Quantum Systems.- 20 The Second Quantization.- 21 Quantum Electro-Magnetic Field – Photons.- 22 Standard Model of Non-relativistic Matter and Radiation.- 23 Theory of Radiation.- 24 Renormalization Group.- 25 Mathematical Supplement: Spectral Analysis.- 26 Mathematical Supplement: The Calculus of Variations.- 27 Comments on Literature, and Further Reading.- References.- Index.
£41.24
Springer Nature Switzerland AG Physics and Finance
Book SynopsisThis book introduces physics students to concepts and methods of finance. Despite being perceived as quite distant from physics, finance shares a number of common methods and ideas, usually related to noise and uncertainties. Juxtaposing the key methods to applications in both physics and finance articulates both differences and common features, this gives students a deeper understanding of the underlying ideas. Moreover, they acquire a number of useful mathematical and computational tools, such as stochastic differential equations, path integrals, Monte-Carlo methods, and basic cryptology. Each chapter ends with a set of carefully designed exercises enabling readers to test their comprehension.Table of ContentsChapter 1 - Introduction Chapter 2 - Concepts of finance Chapter 3 - Portfolio theory and CAPM Chapter 4 - Stochastic processes Chapter 5 - Black-Scholes differential equation Chapter 6 - The Greeks and risk management Chapter 7 - Regression models and hypothesis testing Chapter 8 - Time series Chapter 9 - Bubbles, crashes, fat tails and Levy-stable distributions Chapter 10 - Quantum finance and path integrals Chapter 11 - Optimal control theory.
£54.99
Springer Nature Switzerland AG String Field Theory: A Modern Introduction
Book SynopsisThis textbook provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far due to the exceptional properties of two-dimensional theories, it becomes cumbersome for some questions or even fails at a more fundamental level. These motivations have led to the development of SFT, a description of string theory using the field theory formalism (second-quantization). As a field theory, SFT provides a rigorous and constructive formulation of string theory. The main focus of the book is the construction of the closed bosonic SFT. The accent is put on providing the reader with the foundations, conceptual understanding and intuition of what SFT is. After reading this book, the reader is able to study the applications from the literature. The book is organized in two parts. The first part reviews the notions of the worldsheet theory that are necessary to build SFT (worldsheet path integral, CFT and BRST quantization). The second part starts by introducing general concepts of SFT from the BRST quantization. Then, it introduces off-shell string amplitudes before providing a Feynman diagrams interpretation from which the building blocks of SFT are extracted. After constructing the closed SFT, the author outlines the proofs of several important properties such as background independence, unitarity and crossing symmetry. Finally, the generalization to the superstring is also discussed.Trade Review“The book under review offers a comprehensive self-contained description of string field theory (SFT) and the tools necessary to build it. … For each chapter the author has collected the most relevant references. This, together with various examples, figures, remarks and, especially, a suitable amount of details, has produced a compulsively readable textbook quite useful for students and newcomers. … The last version of the draft of the book can be accessed on the author's professional web page.” (Farhang Loran, Mathematical Reviews, April, 2022)Table of ContentsIntroduction.- Worldsheet path integral: vacuum amplitudes.- Worldsheet path integral: scattering amplitudes.- Worldsheet path integral: complex coordinates.- Conformal field theory in D dimensions.- Conformal field theory on the plane.- CFT systems.- BRST quantization.- String field.- Free BRST string field theory.- Introduction to off-shell string theory.- Geometry of moduli spaces and Riemann surfaces.- Off-shell amplitudes.-Amplitude factorization and Feynman diagrams.- Closed string field theory.- Background independence.- Superstring.- Momentum-space SFT.
£44.99
Springer Nature Switzerland AG Luminescence: Data Analysis and Modeling Using R
Book SynopsisThis book covers applications of R to the general discipline of radiation dosimetry and to the specific areas of luminescence dosimetry, luminescence dating, and radiation protection dosimetry. It features more than 90 detailed worked examples of R code fully integrated into the text, with extensive annotations. The book shows how researchers can use available R packages to analyze their experimental data, and how to extract the various parameters describing mathematically the luminescence signals. In each chapter, the theory behind the subject is summarized, and references are given from the literature, so that researchers can look up the details of the theory and the relevant experiments. Several chapters are dedicated to Monte Carlo methods, which are used to simulate the luminescence processes during the irradiation, heating, and optical stimulation of solids, for a wide variety of materials. This book will be useful to those who use the tools of luminescence dosimetry, including physicists, geologists, archaeologists, and for all researchers who use radiation in their research.Table of Contents1. Introduction.- 2. Analysis and Modeling of TL Data.- 3. Analysis of Experimental OSL Data.- 4. Dose Response of Dosimetric Materials.- 5. Monte Carlo Simulations With Fixed Time Interval.- 6. Luminescence as a Stochastic Life-and-Death Process.- 7. Delocalized Transitions: The R Package RLumCarlo.- 8. Localized Transitions: The R Package RLumCarlo.- 9. Quantum Tunneling and Luminescence Models.- 10. Quantum Tunneling: The R Package RLumCarlo.- 11. Comprehensive Quartz Models Using Program KMS.- 12. Quartz Models Using the R-Package RLumModel.
£66.49
Springer Nature Switzerland AG Gamow Shell Model: The Unified Theory of Nuclear Structure and Reactions
Book SynopsisThis book provides the first graduate-level, self-contained introduction to recent developments that lead to the formulation of the configuration-interaction approach for open quantum systems, the Gamow shell model, which provides a unitary description of quantum many-body system in different regimes of binding, and enables the unification in the description of nuclear structure and reactions. The Gamow shell model extends and generalizes the phenomenologically successful nuclear shell model to the domain of weakly-bound near-threshold states and resonances, offering a systematic tool to understand and categorize data on nuclear spectra, moments, collective excitations, particle and electromagnetic decays, clustering, elastic and inelastic scattering cross sections, and radiative capture cross sections of interest to astrophysics. The approach is of interest beyond nuclear physics and based on general properties of quasi-stationary solutions of the Schrödinger equation – so-called Gamow states. For the benefit of graduate students and newcomers to the field, the quantum-mechanical fundamentals are introduced in some detail. The text also provides a historical overview of how the field has evolved from the early days of the nuclear shell model to recent experimental developments, in both nuclear physics and related fields, supporting the unified description. The text contains many worked examples and several numerical codes are introduced to allow the reader to test different aspects of the continuum shell model discussed in the book.Table of ContentsIntroduction.- The Discrete Spectrum and the Continuum.- One- and Two-Particle Systems.- Shell Model in Berggren Basis.- No-Core Gamow Shell Model.- Unification of Nuclear Structure and Nuclear Reactions.- Collective Phenomena.- Conclusions and Open Problems.
£66.49
Springer Nature Switzerland AG Undecidability, Uncomputability, and
Book SynopsisFor a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.Table of ContentsIntroduction (Aguirre, Merali, Sloan).- Undecidability and Unpredictability: Not Limitations, but Triumphs of Science (Markus Müller).- Indeterminism and Undecidability (Klaas Landsman).- Unpredictability and Randomness (Rade Vuckovac).- Indeterminism, Causality and Information: Has Physics ever been Deterministic? (Flavio Del Santo).- Undecidability, Fractal Geometry and the Unity of Physics (Tim Palmer).- A Gödelian Hunch from Quantum Theory (Hippolyte Dourdent).- Epistemic Horizons: This Sentence is ..... (Jochen Szangolies).- Why is the Universe Comprehensible? (Ian Durham).- Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes (David Wolpert, David Kinney).- Computational Complexity as Anthropic Principle: A Fable (Rick Searle).- Appendix (Aguirre, Merali, Sloan).
£64.99
Springer Nature Switzerland AG Undecidability, Uncomputability, and Unpredictability
Book SynopsisFor a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.Table of ContentsIntroduction (Aguirre, Merali, Sloan).- Undecidability and Unpredictability: Not Limitations, but Triumphs of Science (Markus Müller).- Indeterminism and Undecidability (Klaas Landsman).- Unpredictability and Randomness (Rade Vuckovac).- Indeterminism, Causality and Information: Has Physics ever been Deterministic? (Flavio Del Santo).- Undecidability, Fractal Geometry and the Unity of Physics (Tim Palmer).- A Gödelian Hunch from Quantum Theory (Hippolyte Dourdent).- Epistemic Horizons: This Sentence is ..... (Jochen Szangolies).- Why is the Universe Comprehensible? (Ian Durham).- Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes (David Wolpert, David Kinney).- Computational Complexity as Anthropic Principle: A Fable (Rick Searle).- Appendix (Aguirre, Merali, Sloan).
£64.99
Springer Nature Switzerland AG The Structures of Mathematical Physics: An
Book SynopsisThis textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.Trade Review“This text approaches the reader with shocking breadth and niggardly depth. … Around each definition, there is short---and pleasant---narrative and then a number of examples are described. Chapters end with a list of straightforward exercises … . As a stand-alone mathematical dictionary, the text under review may serve a purpose … .” (Ryan Grady, MAA Reviews, January 30, 2022)Table of ContentsPreface and Acknowledgements.- Sets and Relations.- Mappings and Functions.- Rings and Fields.- Linear Vector Spaces.- Algebras.- Basic Topology and Topological Groups.- Topological Vector Spaces.- Measure, Integration and Hilbert Space.- Operators and Spectra.- Annotated Bibliography and a Guide to Further Reading.- Index.
£54.99
Springer Nature Switzerland AG Numerical Methods for Elliptic and Parabolic
Book SynopsisThis text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.Trade Review“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)Table of ContentsFor Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.
£54.99
Springer Nature Switzerland AG Mathematical Methods in Modern Complexity Science
Book SynopsisThis book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic differential equations, synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems Table of Contents1. Preface by Dr. Dimitri Volchenkov2. Chapter 1 . J. A. Tenreiro Machado, Shannon Information Analysis of the Chromosome Code.3. Chapter 2. Dimitri Volchenkov, Veniamin Smirnov, An Unfair Coin of the Standard & Poor’s 5004. Chapter 3. Relativistic chaotic scattering by Juan D. Bernal, Jesus M. Seoane, Miguel A.F. Sanjuan5. Chapter 4. Artificial Intelligence for Studying Perception of Ambiguous Images and Decision-Marking Processes in the Human Brain by Alexander N. Pisarchik, Anastasija E. Runnova, Nikita S. Frolov, and Alexander E. Hramov6. Chapter 5. Fuhong Min, Chuang Li, Multistability Coexistence of Memristive Chaotic System, and the Application in Image Decryption7. Chapter 6: Veniamin Smirnov, Zhuanzhuan Ma, And Dimitri Volchenkov, Extreme Events and Emergency Scales 8. Chapter 7: M. Edelman, Evolution of Systems with Power-Law Memory: Do We Have to Die?9. Chapter 8: Dimitri Volchenkov, Probability Entanglement and Destructive Interference in Biased Coin Tossing10. Chapter 9: Messoud Efendiev, Vitali Vougalter, On the solvability of some systems of integro-differential equations with drift.11. Chapter 10: Vitali Vougalter, Vitaly Volpert, Solvability in The Sense of Sequences For Some Non Fredholm Operators With The Bi-Laplacian 12. Chapter 11: Vitali Vougalter, The Preservation of Nonnegativity of Solutions of A Parabolic System With The Bi-Laplacian
£104.49
Springer Nature Switzerland AG Holography and Magnetically Induced Phenomena in QCD
Book SynopsisThis book introduces the traditional and novel techniques required to study the thermodynamic and transport properties of quark–gluon plasma. In particular, it reviews the construction of improved holographic models for QCD-like confining gauge theories and their applications in the physics of quark–gluon plasma. It also discusses the recent advances in the development of hydrodynamic techniques, especially those incorporating the effects of external magnetic fields on transport. The book is primarily intended for researchers and graduate students with a background in quantum field theory and particle physics but who may not be familiar with the theory of strong interactions and holographic and hydrodynamic techniques required to study said interactions.Table of ContentsIntroduction: AdS/CFT and heavy ion collisions.- Holographic QCD theories.- Improved holographic QCD - construction of the theory.- Thermodynamics and the confinement/deconfinement transition.- Flavor sector.- Hydrodynamics and transport coefficients.- Hard probes.- ihQCD at finite B.- Conclusion and a look ahead.
£54.99
Springer Nature Switzerland AG Physics with Excel and Python: Using the Same
Book SynopsisThis book is intended to serve as a basic introduction to scientific computing by treating problems from various areas of physics - mechanics, optics, acoustics, and statistical reasoning in the context of the evaluation of measurements. After working through these examples, students are able to independently work on physical problems that they encounter during their studies. For every exercise, the author introduces the physical problem together with a data structure that serves as an interface to programming in Excel and Python. When a solution is achieved in one application, it can easily be translated into the other one and presumably any other platform for scientific computing. This is possible because the basic techniques of vector and matrix calculation and array broadcasting are also achieved with spreadsheet techniques, and logical queries and for-loops operate on spreadsheets from simple Visual Basic macros. So, starting to learn scientific calculation with Excel, e.g., at High School, is a targeted road to scientific computing. The primary target groups of this book are students with a major or minor subject in physics, who have interest in computational techniques and at the same time want to deepen their knowledge of physics. Math, physics and computer science teachers and Teacher Education students will also find a companion in this book to help them integrate computer techniques into their lessons. Even professional physicists who want to venture into Scientific Computing may appreciate this book.Table of Contents
£49.99
Springer Nature Switzerland AG Making Sense of Statistical Mechanics
Book SynopsisMany people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is it all about information? But, if so, then, what is its relation to fluxes of heat?One might ask similar questions about probabilities: Do they express subjective judgments by us, humans, or do they reflect facts about the world, i.e. frequencies. And what notion of probability is used in the natural sciences, in particular statistical mechanics?This book addresses all of these questions in the clear and pedagogical style for which the author is known. Although valuable as accompaniment to an undergraduate course on statistical mechanics or thermodynamics, it is not a standard course book. Instead it addresses both the essentials and the many subtle questions that are usually brushed under the carpet in such courses. As one of the most lucid accounts of the above questions, it provides enlightening reading for all those seeking answers, including students, lecturers, researchers and philosophers of science.Table of ContentsWhat We Need from Thermodynamics.- What Are Probabilities?.- Dynamical Systems.- Statistical Mechanics 1 : The Nature of Equilibrium.- Statistical Mechanics 2: Irreversibility.- Demystifying Entropy.- Comparison with Quantum Mechanics.
£49.99
Springer Nature Switzerland AG A First Course on Symmetry, Special Relativity and Quantum Mechanics: The Foundations of Physics
Book SynopsisThis book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics.Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing.Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.Table of Contents1 Introduction 91.1 The goal of physics . . . . . . . . . . . . . . . . . . . . . . . . 91.2 The connection between physics and mathematics . . . . . . . 101.3 Paradigm shifts . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 The Correspondence Principle . . . . . . . . . . . . . . . . . . 162 Symmetry and Physics 172.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 172.2 What is Symmetry? . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Role of Symmetry in Physics . . . . . . . . . . . . . . . . . . . 182.3.1 Symmetry as a guiding principle . . . . . . . . . . . . . 182.3.2 Symmetry and Conserved Quantities: Noether's Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Symmetry as a tool for simplifying problems . . . . . . 192.4 Symmetries were made to be broken . . . . . . . . . . . . . . 202.4.1 Spacetime symmetries . . . . . . . . . . . . . . . . . . 202.4.2 Parity violation . . . . . . . . . . . . . . . . . . . . . . 212.4.3 Spontaneously broken symmetries . . . . . . . . . . . . 242.4.4 Variational calculations: Lifeguards and light rays . . . 273 Formal Aspects of Symmetry 303.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Symmetries and Operations . . . . . . . . . . . . . . . . . . . 303.2.1 Denition of a symmetry operation . . . . . . . . . . . 303.2.2 Rules obeyed by symmetry operations . . . . . . . . . 323.2.3 Multiplication tables . . . . . . . . . . . . . . . . . . . 353.2.4 Symmetry and group theory . . . . . . . . . . . . . . . 363.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 The identity operation . . . . . . . . . . . . . . . . . . 373.3.2 Permutations of two identical objects . . . . . . . . . . 373.3.3 Permutations of three identical objects . . . . . . . . . 383.3.4 Rotations of regular polygons . . . . . . . . . . . . . . 393.4 Continuous vs discrete symmetries . . . . . . . . . . . . . . . 403.5 Symmetries and Conserved Quantities:Noether's Theorem . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Supplementary: Variational Mechanics and the Proof of Noether'sTheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Variational Mechanics: Principle of Least Action . . . . 423.6.2 Euler-Lagrange Equations . . . . . . . . . . . . . . . . 473.6.3 Proof of Noether's Theorem . . . . . . . . . . . . . . . 484 Symmetries and Linear Transformations 524.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Review of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.1 Coordinate free denitions . . . . . . . . . . . . . . . . 534.2.2 Cartesian Coordinates . . . . . . . . . . . . . . . . . . 584.2.3 Vector operations in component form . . . . . . . . . . 594.2.4 Position vector . . . . . . . . . . . . . . . . . . . . . . 604.2.5 Dierentiation of vectors: velocity and acceleration . . 624.3 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . 634.3.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.2 Translations . . . . . . . . . . . . . . . . . . . . . . . . 644.3.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 Linear Transformations and matrices . . . . . . . . . . . . . . 684.4.1 Linear transformations as matrices . . . . . . . . . . . 684.4.2 Identity Transformation and Inverses . . . . . . . . . . 704.4.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 704.4.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 724.4.5 Matrix Representation of Permutations of Three Objects 734.5 Pythagoras and Geometry . . . . . . . . . . . . . . . . . . . . 745 Special Relativity I: The Basics 775.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2.1 Frames5.2.2 Spacetime Diagrams . . . . . . . . . . . . . . . . . . . 785.2.3 Newtonian Relativity and Galilean Transformations . . 835.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 The Fundamental Postulate . . . . . . . . . . . . . . . 855.3.2 The problem with Galilean Relativity . . . . . . . . . . 855.3.3 Michelson-Morley Experiment . . . . . . . . . . . . . . 875.3.4 Maxwell's Equations . . . . . . . . . . . . . . . . . . . 905.4 Summary of Consequences . . . . . . . . . . . . . . . . . . . . 915.5 Relativity of Simultaneity . . . . . . . . . . . . . . . . . . . . 925.6 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.6.1 Derivation: . . . . . . . . . . . . . . . . . . . . . . . . 975.6.2 Proper Time . . . . . . . . . . . . . . . . . . . . . . . . 995.6.3 Experimental Conrmation . . . . . . . . . . . . . . . 1015.6.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 1025.7 Lorentz Contraction . . . . . . . . . . . . . . . . . . . . . . . 1045.7.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.3 Proper Length and Proper Distance. . . . . . . . . . . 1045.7.4 Examples: . . . . . . . . . . . . . . . . . . . . . . . . . 1056 Special Relativity II: In Depth 1106.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1106.2 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . 1106.2.1 Derivation of general form . . . . . . . . . . . . . . . . 1106.2.2 Properties of Lorentz Transformations . . . . . . . . . 1136.2.3 Lorentzian Geometry . . . . . . . . . . . . . . . . . . . 1166.3 The Light Cone . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.4 Proper time revisited . . . . . . . . . . . . . . . . . . . . . . . 1206.5 Relativistic Addition of Velocities . . . . . . . . . . . . . . . . 1226.6 Relativistic Doppler Shift . . . . . . . . . . . . . . . . . . . . . 1246.6.1 Non-relativistic Doppler Shift Review . . . . . . . . . . 1246.6.2 Relativistic Doppler Shift . . . . . . . . . . . . . . . . 1246.7 Relativistic Energy and Momentum . . . . . . . . . . . . . . . 1276.7.1 Relativistic Energy Momentum Conservation . . . . . . 1276.7.2 Relativistic Inertia . . . . . . . . . . . . . . . . . . . . 1286.7.3 Relativistic Energy . . . . . . . . . . . . . . . . . . . . 1296.7.4 Relativistic Three-Momentum . . . . . . . . . . . . . . 1296.7.5 Relationship Between Relativistic Energy and Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.7.6 Kinetic energy: . . . . . . . . . . . . . . . . . . . . . . 1306.7.7 Massless particles . . . . . . . . . . . . . . . . . . . . 1316.8 Space-time Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1336.8.1 Position Four-Vector: . . . . . . . . . . . . . . . . . . . 1346.8.2 Four-momentum: . . . . . . . . . . . . . . . . . . . . . 1356.8.3 Null four-vectors . . . . . . . . . . . . . . . . . . . . . 1376.8.4 Relativistic Scattering . . . . . . . . . . . . . . . . . . 1376.8.5 More Examples . . . . . . . . . . . . . . . . . . . . . . 1386.9 Relativistic Units . . . . . . . . . . . . . . . . . . . . . . . . . 1396.10 Symmetry Redux . . . . . . . . . . . . . . . . . . . . . . . . . 1406.10.1 Matrix form of Lorentz Transformations . . . . . . . . 1406.10.2 Lorentz Transformations as a Symmetry Group . . . . 1426.11 Supplementary: Four vectors and tensors in covariant form . . 1437 General Relativity 1497.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 Problems with Newtonian Gravity . . . . . . . . . . . . . . . . 1497.2.1 Review of Newtonian Gravity . . . . . . . . . . . . . . 1497.2.2 Perihelion Shift of Mercury . . . . . . . . . . . . . . . 1517.2.3 Action at a Distance . . . . . . . . . . . . . . . . . . . 1527.2.4 The Puzzle of Inertial vs Gravitational Mass . . . . . . 1537.3 Einstein's Thinking: the Strong Principle of Equivalence . . . 1537.4 Geometry of Spacetime . . . . . . . . . . . . . . . . . . . . . . 1557.5 Some Consequences of General Relativity: . . . . . . . . . . . 1587.6 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . 1597.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1597.6.2 Detection . . . . . . . . . . . . . . . . . . . . . . . . . 1607.6.3 Recent Observations . . . . . . . . . . . . . . . . . . . 1617.7 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1647.7.4 Further Information . . . . . . . . . . . . . . . . . . . 1667.8 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668 Introduction to the Quantum 1708.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1708.2 Light as particles . . . . . . . . . . . . . . . . . . . . . . . . . 1718.2.1 Review: Light as Waves . . . . . . . . . . . . . . . . . 1718.2.2 Photoelectric Eect . . . . . . . . . . . . . . . . . . . . 1718.2.3 Compton Scattering . . . . . . . . . . . . . . . . . . . 1758.3 Blackbody Radiation and the Ultraviolet Catastrophe . . . . . 1798.3.1 Blackbody Radiation . . . . . . . . . . . . . . . . . . . 1798.3.2 Derivation of Rayleigh-Jeans Law . . . . . . . . . . . . 1818.3.3 The ultraviolet catastrophe . . . . . . . . . . . . . . . 1888.3.4 Quantum resolution: . . . . . . . . . . . . . . . . . . . 1898.3.5 The Early Universe: the ultimate blackbody . . . . . . 1918.4 Particles as waves . . . . . . . . . . . . . . . . . . . . . . . . . 1968.4.1 Electron waves . . . . . . . . . . . . . . . . . . . . . . 1968.4.2 de Broglie Wavelength . . . . . . . . . . . . . . . . . . 1978.4.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1998.5 The Heisenberg Uncertainty Principle . . . . . . . . . . . . . . 2029 The Wave Function 2049.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 2049.2 Quantum vs Newtonian description of physical states . . . . . 2049.2.1 Newtonian description of the state of a particle . . . . 2059.2.2 Quantum description of the state of a particle . . . . . 2059.3 Physical Consequences and Interpretation . . . . . . . . . . . 2079.4 Measurements of position . . . . . . . . . . . . . . . . . . . . 2089.5 Example: Gaussian wavefunction . . . . . . . . . . . . . . . . 2099.6 \Spooky" Action at a Distance: Non-Locality in QuantumMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.6.1 The EPR \Paradox" . . . . . . . . . . . . . . . . . . . 2119.6.2 Bell's Theorem and the Experimental Repudiation ofEPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21410 The Schrodinger Equation 21710.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 21710.2 Momentum in Quantum Mechanics . . . . . . . . . . . . . . . 21810.2.1 Pure Waves . . . . . . . . . . . . . . . . . . . . . . . . 21810.2.2 The Momentum Operator . . . . . . . . . . . . . . . . 22010.3 Energy in Quantum Mechanics . . . . . . . . . . . . . . . . . 22310.4 The Time Independent Schrodinger Equation . . . . . . . . . 22410.4.1 Stationary States . . . . . . . . . . . . . . . . . . . . . 22410.4.2 The \Quantum" in Quantum Mechanics . . . . . . . . 22610.5 Examples of Stationary States . . . . . . . . . . . . . . . . . . 22610.5.1 Free particle in one dimension . . . . . . . . . . . . . . 22610.5.2 Example 2: Particle in a Box with Impenetrable Walls 22710.5.3 Example 3 : Simple Harmonic Oscillator . . . . . . . . 22910.6 Absorption and emission . . . . . . . . . . . . . . . . . . . . . 23110.7 Tunnelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23310.7.1 Tunnelling through a potential barrier of nite width . 23310.7.2 Particle in a Box with Penetrable Walls . . . . . . . . . 23510.7.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 23710.7.4 Applications of tunnelling . . . . . . . . . . . . . . . . 23810.8 The Quantum Correspondence Principle . . . . . . . . . . . . 24210.8.1 Recovering the everyday world . . . . . . . . . . . . . . 24210.8.2 The Bohr Correspondence Principle . . . . . . . . . . . 24310.9 The Time Dependent Schrodinger equation . . . . . . . . . . . 24410.9.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 24611 The Hydrogen Atom 24911.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 24911.2 Newtonian (Classical) Dynamics . . . . . . . . . . . . . . . . . 24911.3 The Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . . . . 25111.4 Semi-classical spectrum from the Bohr correspondence principle25411.5 Emission and Absorption Spectra . . . . . . . . . . . . . . . . 25411.6 Three Dimensional Hydrogen Atom . . . . . . . . . . . . . . . 25611.6.1 Schrodinger Equation . . . . . . . . . . . . . . . . . . . 25611.6.2 Solutions and Quantum Numbers . . . . . . . . . . . . 25811.6.3 Fermions and the spin quantum number . . . . . . . . 26211.7 Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 26511.7.1 Hydrogen-like atoms . . . . . . . . . . . . . . . . . . . 26511.7.2 Chemical Properties and the Periodic Table . . . . . . 26612 Nuclear Physics 27012.1 Properties of the Nucleus . . . . . . . . . . . . . . . . . . . . . 27012.1.1 Mass of Nucleons . . . . . . . . . . . . . . . . . . . . . 27012.1.2 Structure of Nucleus . . . . . . . . . . . . . . . . . . . 27112.1.3 The Nuclear Force . . . . . . . . . . . . . . . . . . . . 27112.2 Binding Energy and Stability . . . . . . . . . . . . . . . . . . 27412.2.1 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . 27412.2.2 Binding Energy . . . . . . . . . . . . . . . . . . . . . . 27512.2.3 Binding Energy per Nucleon . . . . . . . . . . . . . . . 27512.3 Formation of Elements: A Brief History of the Universe . . . . 27612.4 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 27912.4.1 Unstable Isotopes . . . . . . . . . . . . . . . . . . . . . 27912.4.2 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 28112.4.3 Beta decay . . . . . . . . . . . . . . . . . . . . . . . . . 28212.4.4 Alpha Decay . . . . . . . . . . . . . . . . . . . . . . . 28312.4.5 Decay Rates . . . . . . . . . . . . . . . . . . . . . . . . 28312.4.6 Carbon Dating . . . . . . . . . . . . . . . . . . . . . . 28513 Supplementary: Advanced Topics 28713.1 Quantum Information and Quantum Computation . . . . . . . 28713.2 Relativity and quantum mechanics . . . . . . . . . . . . . . . 28714 Conclusions 28815 Appendix: Mathematical Background 28915.1 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . 28915.2 Probabilities and expectation values . . . . . . . . . . . . . . . 29115.2.1 Discrete Distributions . . . . . . . . . . . . . . . . . . 29115.2.2 Continuous probability distributions . . . . . . . . . . 29215.2.3 Dirac Delta Function . . . . . . . . . . . . . . . . . . . 29615.3 Supplementary: Fourier Series and Transforms . . . . . . . . . 29815.3.1 Fourier series . . . . . . . . . . . . . . . . . . . . . . . 29815.3.2 Fourier Transforms . . . . . . . . . . . . . . . . . . . . 30015.3.3 The mathematical uncertainty principle . . . . . . . . . 30215.3.4 Dirac Delta Function Revisited . . . . . . . . . . . . . 30315.3.5 Parseval's Theorem . . . . . . . . . . . . . . . . . . . . 30315.4 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30415.4.1 Moving pure waves . . . . . . . . . . . . . . . . . . . . 30415.4.2 Complex Waves . . . . . . . . . . . . . . . . . . . . . . 30515.4.3 Group velocity and phase velocity . . . . . . . . . . . 30515.4.4 Wave packets . . . . . . . . . . . . . . . . . . . . . . . 30715.4.5 Wave number and momentum . . . . . . . . . . . . . . 30915.5 Derivation of Hydrogen Wave Functions . . . . . . . . . . . . 312
£66.49
Springer Nature Switzerland AG Supernovae, Neutron Star Physics and Nucleosynthesis
Book SynopsisThis book deals with the interdisciplinary areas of nuclear physics, supernovae and neutron star physics. It addresses the physics and astrophysics of the spectacular supernova explosions, starting with the collapse of massive stars and ending with the birth of neutron stars or black holes. Recent progress in the understanding of core collapse supernova (CCSN) and observational aspects of future detections of neutrinos from CCSN explosions are discussed. The other main focus in this text is the novel phases of dense nuclear matter, its compositions and equation of state (EoS) from low to very high baryon density relevant to supernovae and neutron stars. The multi-messenger astrophysics of binary neutron star merger GW170817 and its relation to EoS through tidal deformability are also presented in detail. The synthesis of elements heavier than iron in the supernova and neutron star environment by the rapid (r)-process are treated here with special emphasis on the nucleosynthesis in the ejected material from GW170817. This monograph is written for graduate students and researchers in the field of nuclear astrophysics.Table of ContentsPREFACE1. INTRODUCTION 2. THEORY OF SUPERNOVA EXPLOSIONS 2.1 Overview- historical 2.2 Supernova Type Ia 2.3 Gravitational collapse and pre-supernova conditions 2.4 Production of neutrinos and their emission 2.5 Shock wave formation and its eventual stalling 2.6 The revival of the shock wave- the neutrino mechanism 2.7 Multi-dimensional hydrodynamic simulations and the present scenario 2.8 The supernova SN1987A 2.9 Detection of neutrinos from future supernova events 3. NEUTRON STARS 3.1 History and discovery of neutron stars 3.2 Observational Constraints on neutron stars 3.3 Compositions and novel phases of neutron stars - crust to core 3.4 Equation of State (EoS) models of neutron star matter 3.5 Relativistic field theoretical models for dense matter at zero and finite temperatures 3.6 Tolman-Oppenheimer-Volkoff Equation and Structures of neutron stars 3.7 A stable branch of compact stars beyond neutron star 3.8 Rotating neutron stars, moment of inertia (I) and quadrupole moment (Q) 3.9 Neutron star matter in strongly quantizing magnetic fields 3.10 EoS tables for supernova and binary neutron star merger simulations 4. BINARY NEUTRON STAR MERGERS 4.1 Gravitational waves as new window into neutron stars 4.2 First binary neutron star (BNS) merger GW170817 and multi-messenger astrophysics 4.3 Tidal deformability, LOVE number and EoS 4.4 I-Love-Q universal relations 4.5 Late inspiral phase of BNS merger, tidal deformability and cold EoS 4.6 Neutron Star radius determination from tidal deformability 4.7 Hot and neutrino trapped merger remnant and finite temperature EoS 5. SYNTHESIS OF HEAVY ELEMENTS IN THE UNIVERSE 5.1 s-, r- and p-processes 5.2 Conditions for production of elements by r- process and the sites 5.3 Electromagnetic counterpart of GW170817 and ejected matter in BNS merger 5.4 Decompression of ejected neutron rich matter in Lattimer and Schramm model 5.5 Kilonova model 5.6 Heavy element synthesis in neutron rich matter ejected in GW170817 INDEX BIBLIOGRAPHY (eventually at chapter-ends)
£44.99
Springer Nature Switzerland AG Supernovae, Neutron Star Physics and Nucleosynthesis
Book SynopsisThis book deals with the interdisciplinary areas of nuclear physics, supernovae and neutron star physics. It addresses the physics and astrophysics of the spectacular supernova explosions, starting with the collapse of massive stars and ending with the birth of neutron stars or black holes. Recent progress in the understanding of core collapse supernova (CCSN) and observational aspects of future detections of neutrinos from CCSN explosions are discussed. The other main focus in this text is the novel phases of dense nuclear matter, its compositions and equation of state (EoS) from low to very high baryon density relevant to supernovae and neutron stars. The multi-messenger astrophysics of binary neutron star merger GW170817 and its relation to EoS through tidal deformability are also presented in detail. The synthesis of elements heavier than iron in the supernova and neutron star environment by the rapid (r)-process are treated here with special emphasis on the nucleosynthesis in the ejected material from GW170817. This monograph is written for graduate students and researchers in the field of nuclear astrophysics.Table of ContentsPREFACE1. INTRODUCTION 2. THEORY OF SUPERNOVA EXPLOSIONS 2.1 Overview- historical 2.2 Supernova Type Ia 2.3 Gravitational collapse and pre-supernova conditions 2.4 Production of neutrinos and their emission 2.5 Shock wave formation and its eventual stalling 2.6 The revival of the shock wave- the neutrino mechanism 2.7 Multi-dimensional hydrodynamic simulations and the present scenario 2.8 The supernova SN1987A 2.9 Detection of neutrinos from future supernova events 3. NEUTRON STARS 3.1 History and discovery of neutron stars 3.2 Observational Constraints on neutron stars 3.3 Compositions and novel phases of neutron stars - crust to core 3.4 Equation of State (EoS) models of neutron star matter 3.5 Relativistic field theoretical models for dense matter at zero and finite temperatures 3.6 Tolman-Oppenheimer-Volkoff Equation and Structures of neutron stars 3.7 A stable branch of compact stars beyond neutron star 3.8 Rotating neutron stars, moment of inertia (I) and quadrupole moment (Q) 3.9 Neutron star matter in strongly quantizing magnetic fields 3.10 EoS tables for supernova and binary neutron star merger simulations 4. BINARY NEUTRON STAR MERGERS 4.1 Gravitational waves as new window into neutron stars 4.2 First binary neutron star (BNS) merger GW170817 and multi-messenger astrophysics 4.3 Tidal deformability, LOVE number and EoS 4.4 I-Love-Q universal relations 4.5 Late inspiral phase of BNS merger, tidal deformability and cold EoS 4.6 Neutron Star radius determination from tidal deformability 4.7 Hot and neutrino trapped merger remnant and finite temperature EoS 5. SYNTHESIS OF HEAVY ELEMENTS IN THE UNIVERSE 5.1 s-, r- and p-processes 5.2 Conditions for production of elements by r- process and the sites 5.3 Electromagnetic counterpart of GW170817 and ejected matter in BNS merger 5.4 Decompression of ejected neutron rich matter in Lattimer and Schramm model 5.5 Kilonova model 5.6 Heavy element synthesis in neutron rich matter ejected in GW170817 INDEX BIBLIOGRAPHY (eventually at chapter-ends)
£29.99
Springer Nature Switzerland AG Feynman Integrals: A Comprehensive Treatment for Students and Researchers
Book SynopsisThis textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics. Feynman integrals are indispensable for precision calculations in quantum field theory. At the same time, they are also fascinating from a mathematical point of view. Topics from quantum field theory and advanced mathematics are introduced as needed. The book covers modern developments in the field of Feynman integrals. Topics included are: representations of Feynman integrals, integration-by-parts, differential equations, intersection theory, multiple polylogarithms, Gelfand-Kapranov-Zelevinsky systems, coactions and symbols, cluster algebras, elliptic Feynman integrals, and motives associated with Feynman integrals. This volume is aimed at a) students at the master's level in physics or mathematics, b) physicists who want to learn how to calculate Feynman integrals (for whom state-of-the-art techniques and computations are provided), and c) mathematicians who are interested in the mathematical aspects underlying Feynman integrals. It is, indeed, the interwoven nature of their physical and mathematical aspects that make Feynman integrals so enthralling.Trade Review“This book provides a detailed and up-to-date introduction to Feynman integrals … . The book is written in a very didactic way. … the book gives an excellent introduction to the field of Feynman integrals at the level of a master's/starting Ph.D. student … . The structure of the book and the fact that it contains many exercises make it a very useful resource for a course on this topic.” (Samuel Abreu, Mathematical Reviews, December, 2023)Table of ContentsThe file is attached
£39.99
Springer International Publishing AG Complex Integration: A Compendium of Smart and Little-Known Techniques for Evaluating Integrals and Sums
Book SynopsisIntegrals and sums are not generally considered for evaluation using complex integration. This book proposes techniques that mainly use complex integration and are quite different from those in the existing texts. Such techniques, ostensibly taught in Complex Analysis courses to undergraduate students who have had two semesters of calculus, are usually limited to a very small set of problems. Few practitioners consider complex integration as a tool for computing difficult integrals. While there are a number of books on the market that provide tutorials on this subject, the existing texts in this field focus on real methods. Accordingly, this book offers an eye-opening experience for computation enthusiasts used to relying on clever substitutions and transformations to evaluate integrals and sums. The book is the result of nine years of providing solutions to difficult calculus problems on forums such as Math Stack Exchange or the author's website, residuetheorem.com. It serves to detail to the enthusiastic mathematics undergraduate, or the physics or engineering graduate student, the art and science of evaluating difficult integrals, sums, and products.Table of Contents1. Review of foundational concepts1.1. Sequences and Series 1.1.1. Sequences of Real Numbers and their Series – sequences, limits, series, convergence, harmonic numbers, summation by parts, change in the order of summation 1.1.2. Power Series and Generating Functions – definitions, radius of convergence, generating function representations of sequences, convolution 1.2. Integrals 1.2.1. Riemann Sums – definition, direct evaluation of certain sums 1.2.2. Fundamental Theorem - definition of definite integral, statement of theorem, verifications 1.2.3. Multiple Integrals – double integrals, conditions for reversal or order of integration 1.3. Evaluation Techniques 1.3.1. Integration by Parts - review 1.3.2. Conversion to Multiple Integrals – “Feynman’s Technique,” replacing a portion of an integrand with an integral representation and reversing the order of integration 1.3.3. Green’s Theorem – review, path integrals and parametrization, Stokes’ Theorem, applications 1.3.4. Partial Fractions review 1.4. Problems 2. Complex Integration 2.1. Analytic Functions 2.1.1. Cauchy-Riemann Conditions – complex functions and their derivatives, defining analytic functions as a direction-independent derivative, harmonic functions 2.1.2. Evaluating Complex Integrals – numerical examples of parametrizations 2.1.3. Path Independence – demonstrate for analytic functions and demonstrate invalidity for nonanalytic integrands 2.2. Cauchy’s Theorems 2.2.1. Winding Numbers – definition in terms of a complex integral 2.2.2. Cauchy’s Integral Theorem – derivation and illustration for a wide variety of integrands and contours 2.2.3. Cauchy’s Theorem – statement, examples, Liouville’s Theorem, Morera’s Theorem 2.3. Useful Results 2.3.1. Taylor Series – review, error analysis in complex plane, convergence 2.3.2. Laurent Series – regions of validity (e.g., annuli), analytic continuation 2.3.3. Argument Principle – derivation for zeroes and poles 2.3.4. Rouche’s Theorem – derivation, illustration for determining poles within integration contours 2.4. Multivalued Functions – branch points, branch cuts, Riemann surfaces 2.5. Problems 3. Evaluation of Real Integrals and Sums 3.1. Preliminary Matters 3.1.1. Poles and Residue Theory – residue definition, residue computation 3.1.2. Essential Singularities – computation of residues of essential singularities 3.1.3. Branch Points – illustration of a unified approach to expressing an integral of a function in terms of its singularities 3.2. Definite Integrals 3.2.1. Integrands Having Both Poles and Branch Points – e.g., integrands featuring logs and exponents less than -1 3.2.2. Integrands Defined Over - insertion of one higher power of log(z) in the integrand, residue backpropagation 3.2.3. Integrands Having Rational Functions of Polynomials and Trigonometric Functions – integration over the unit circle, modifying the unit circle in the presence of singularities, replacing monomial with a branch point in constructing a contour integral 3.2.4. Alternative Contours: Wedges, Rectangles, and Others – reducing the number of singularities in a contour to simplify calculation 3.2.5. Integrands Having Algebraic Functions and the Residue At Infinity – whole new paradigm in evaluating definite integrals with finite limits of an integrand having branch points at the finite limits, defining the residue at infinity, branch point at infinity 3.3. Sums 3.3.1. Complex Integral Representations – selection of integrand and contour to produce sums, demonstration of convergence of complex integral as contour expands to infinity 3.3.2. Examples – rational summands, summands with trigonometric functions 3.4. Problems 4. Cauchy Principal Value 4.1. Integrands Having Poles On the Contour 4.1.1. Definition of a Cauchy Principal Value – definition as a limit, illustration with simple examples 4.1.2. Managing Divergent Terms of a Contour Integral – detailed illustrations of evaluating definite integrals via complex integrals having contributions with divergent terms that cancel 4.2. Analytic Signals and Hilbert Transforms – equivalence of Cauchy-Riemann equations and Hilbert transforms of real and imaginary parts of an analytic function, illustrations of analytic signals having harmonic real and imaginary parts, examples of deriving imaginary parts of analytic function from real part 4.3. Problems 5. Integral Transforms 5.1. Preliminary Matters 5.1.1. The Dirac Delta Function – derivation via self-transform in Hilbert transform integrals, review of properties 5.1.2. A General Discussion of Integral Transforms - integral transforms require a computable inverse to be of any use, conditions under which inverses exist, general format of integral transforms 5.2. The Fourier Transform 5.2.1. Definition and Plancherel’s Theorem – mean square error, and inner product spaces, the Fourier Transform as a Principal Value 5.2.2. Jordan’s Lemma – evaluating Fourier integrals using complex integration, convergence conditions 5.2.3. Parseval’s Theorem – statement, examples of integral evaluations, Fourier series and application of theorem to sums 5.2.4. Convolution Theorem – statement and derivation, applications 5.2.5. Analyticity of the Fourier Transform In the Complex Plane - theorem relating rates of convergence of Fourier transforms and their inverses in the complex plane, strips of convergence, causality 5.2.6. Poisson Sum Formula – derivation, application to computation of error function to machine precision anywhere in the complex plane 5.3. The Laplace Transform 5.3.1. Definition – extending the discussion of analyticity of the Fourier transform with an exponentially decaying kernel rather than an oscillatory kernel, derivation of inverse as an integral in the complex plane 5.3.2. Convolution Theorem – derivation, examples, application to computing certain classes of definite integrals 5.3.3. Inversion Via Complex Integration 5.3.3.1. Solutions to Ordinary Differential Equations and Rational Transforms – initial conditions, homogeneous and inhomogeneous equations, inversion via the residue theorem 5.3.3.2. Solutions to Partial Differential Equations and Multivalued Transforms – heat equation produces multivalued transforms, evaluation of inverse Laplace transforms to derive solutions 5.4. The Mellin Transform 5.4.1. Definition discussion of strip of convergence, inverse Mellin transform 5.4.2. Convolution Theorem – derivation; NB this will be used in the next chapter 5.4.3. Scaling – expression of scaled integrals in terms of residues 5.5. Problems 6. Asymptotic Analysis 6.1. Definitions 6.1.1. Big-O, Little-O, and The Squiggle – i.e., definitions of asymptotic equivalence in specific limits 6.1.2. Asymptotic Series – definition, properties, numerical calculations, summation acceleration techniques 6.2. Integration by Parts – development of asymptotic series; limitations 6.2.1. Euler-Maclurin Formula – derivation of asymptotic series using integration by parts, application to evaluation of sums 6.3. Watson’s Lemma and h-Transforms – asymptotic behavior of monotonic integrands, application of Mellin transforms in derivation 6.3.1. Application to Complex Integration – evaluation of integrals with branch points at infinity using h-transforms 6.4. Laplace’s Method – asymptotic behavior of nonmonotomic, nonoscillatory integrals 6.5. The Method of Steepest Descents – deriving asymptotic behavior of complex integrals, derive behavior of real integrals by using Cauchy’s Theorem 6.6. Problems
£27.99
£71.24
Springer Levoluzione del pensiero scientifico dallantica Grecia ai giorni nostri
Book SynopsisDa Esiodo ad Orazio.- 2 Sull'unità della conoscenza.- 3 Archelao.- 4 Sulle tracce di Pitagora.- 5 Dio salvi Ippaso!.- 6 Gli atomi geometrici non esistono.- 7 Su filosofia e scienza.- 8 Filosofia e condizione femminile.- 9 La terza parte.- 10 Eudosso di Cnido.- 11 Archimede e la scienza.- 12 Arte e scienza.- 13 Sul ruolo del De Rerum Natura.- 14 Roghi di persone, di libri e di idee.- 15 Dante, i matematici ed i filosofi.- 16 Ma perché si chiama "seno"?.- 17 Un gesuita euclideo.- 18 Contare gli atomi?.- 19 Le radici del metodo scientifico.- 20 Ancora sul metodo scientifico.- 21 Scienza greca (o no?).- 22 Dai suoni all'antimateria.- A I poliedri regolari.- B Scala pitagorica.- C Medie pitagoriche.- D La grandezza degli atomi.- E I blocchi della piramide.- F Sulla nozione di numero reale.- G Sulla congettura di Archimede.- H Alcune illusioni ottiche.- Ringraziamenti.- Riferimenti bibliografici.- Indice delle persone.
£24.99
Springer Calculus of Variations on Fibred Manifolds and Variational Physics
Book SynopsisChapter 1. Introduction.- Chapter 2. Fibred manifolds.- Chapter 3. Vector fields and differential forms.- Chapter 4. Calculus of variations.- Chapter 5. Dynamical forms and the inverse problem.- Chapter 6. Hamiltonian systems.- Chapter 7. Elements of the variational sequences.- Chapter 8. Extension: Geometrical structures for field theories.- Chapter 9. Variational physics.- Chapter 10. Appendix.
£64.99
Springer Viaggio nella fisica moderna
Book SynopsisIntroduction.- Capitolo 1 La teoria della Relatività di Einstein: una nuova visione del mondo.- Capitolo 2 La Meccanica Quantistica: il bizzarro mondo atomico e subatomico.- Capitolo 3 Materia condensata e l'impatto tecnologico della prima rivoluzione quantistica.- Capitolo 4 La seconda rivoluzione quantistica e le tecnologie quantistiche.
£29.44
£132.28
£208.99
£132.99
Springer What is a Fluctuation Theorem
Book SynopsisIntroduction.- Fluctuations Relations and Large Deviations.- Examples.- Two Fluctuation Theorems for Chaotic Maps.- Examples.
£64.99
Birkhauser Verlag AG The Navier-Stokes Equations: An Elementary Functional Analytic Approach
Book SynopsisThe primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.Trade ReviewFrom the reviews:“The book is well written and not unnecessarily wordy. There is an up-to-date bibliography and a nice index. … a mathematician who wishes to know what the important issues concerning eq. (1) are and what has been achieved, would find this an excellent source. Equally, a mathematically-minded student, with a good grounding in analysis and who has decided to work in this area, or the teacher who wants to teach a course on this material would find this a valuable text.” (P. N. Shankar,Current Science, Vol. 85 (2), July, 2003)Table of ContentsPreliminary Results.- The Stationary Navier-Stokes Equations.- The Linearized Nonstationary Theory.- The Full Nonlinear Navier-Stokes Equations.
£75.99
De Gruyter Nonlinear Dynamics
Book SynopsisMany nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities, provides a richly illustrated introduction to nonlinear dynamical systems and chaos and a solid foundation for this fascinating subject. It will satisfy those who want discover this field, including at the undergraduate level, but also those who need a compact and consistent overview, gathering the concepts essential to nonlinear scientists.The first and second chapters describe the essential concepts needed to describe nonlinear dynamical systems as well as their stability. The third chapter introduces the concept of bifurcation, where the qualitative dynamical behavior of a system changes. The fourth chapter deals with oscillations, from their birth to their destabilization, and how they respond to external driving. The fifth and sixth chapters discuss complex behaviors that only occur in state spaces of dimension three and higher: quasi-periodicity and chaos, from their general properties to quantitative methods of characterization. All chapters are supplemented by exercises ranging from direct applications of the notions introduced in the corresponding chapter to elaborate problems involving concepts from different chapters, as well as numerical explorations.
£47.02
De Gruyter Quantum Technologies: For Engineers
Book SynopsisHow does a quantum computer work and how can photons be used to transmit messages securely? Intended for engineering and computer science students, this introduction to quantum technologies presents the fundamentals of quantum computing, quantum communication, and quantum sensing without requiring extensive previous knowledge of physics.
£42.75
De Gruyter Data Management for Natural Scientists: A Practical Guide to Data Extraction and Storage Using Python
Book SynopsisData Management for Natural Scientists offers a practical guide for scientific processing of data. It covers the way from “getting hands on” experimental results to ensuring their use for addressing various scientific questions. Code snippets are provided in order to introduce the proposed workstream and to demonstrate the adjustability to specific challenges.
£54.62
De Gruyter Klassische und erweiterte Dimensionsanalyse
£60.32
Springer International Publishing AG Special Relativity
Book SynopsisThis book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski space-time. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its co-variant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates.Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.Trade ReviewFrom the reviews:“The book is one of the best texts in special relativity designed for readers between the college-level and advanced level. … A number of useful and new examples is added at the end of every chapter of the book. … A very useful table of constants is added at the end of the book. … The book represents one of the best conspects in special relativity and is useful for professors of special relativity. It is good for students and every other reader.” (Alex Gaina, zbMATH, Vol. 1277, 2014)Table of ContentsFundamentals of Special Relativity.- Introduction.- The Principle of Relativity.- Groups—the Galilei group.- Galileian law of addition of velocities.- The lesson from electromagnetism.- The postulates of Special Relativity.- Consequences of the postulates.- Conclusion.- Problems.- The Lorentz transformation.- Introduction.- The Lorentz transformation.- Derivation of the Lorentz transformation.- Mathematical properties of the Lorentz transformation.- Absolute speed limit and causality.- Length contraction from the Lorentz transformation.- Time dilation from the Lorentz transformation.- Transformation of velocities and accelerations in Special Relativity.- Matrix representation of the Lorentz transformation.- The Lorentz group.- The Lorentz transformation as a rotation by an imaginary angle with imaginary time.- The GPS system.- Conclusion.- Problems.- The 4-dimensional world view.- Introduction.- The 4-dimensional world.- Spacetime diagrams.- Conclusion.- Problems.- The formalism of tensors.- Introduction.- Vectors and tensors.- Contravariant and covariant vectors.- Contravariant and covariant tensors.- Tensor algebra.- Tensor fields.- Index-free description of tensors.- The metric tensor.- The Levi-Civita symbol and tensor densities.- Conclusion.- Problems.- Tensors in Minkowski spacetime.- Introduction.- Vectors and tensors in Minkowski spacetime.- The Minkowski metric.- Scalar product and length of a vector in Minkowski spacetime.- Raising and lowering tensor indices.- Causal nature of 4-vectors.- Hypersurfaces.- Gauss’ theorem.- Conclusion.- Problems.- Relativistic mechanics.- Introduction.- Relativistic dynamics of massive particles.- The relativistic force.- Angular momentum of a particle.- Particle systems.- Conservation of mass-energy.- Conclusion.- Problems.- Relativistic optics.- Introduction.- Relativistic optics: null rays.- The drag effect.- The Doppler effect.- Aberration.- Relativistic beaming.- Visual appearance of extended objects.- Conclusion.- Problems.- Measurements in Minkowski spacetime.- Introduction.- Energy of a particle measured by an observer.- Frequency measured by an observer.- A more systematic treatment of measurement.- The 3+1 splitting.- Conclusion.- Problems.- Matter in Minkowski spacetime.- Introduction.- The energy-momentum tensor.- Covariant conservation.- Energy conditions.- Angular momentum.- Perfect fluids.- The scalar field.- The electromagnetic field.- Conclusion.- Problems.- Special Relativity in arbitrary coordinates.- Introduction.- The covariant derivative.- Spacetime curves and covariant derivative.- Physics in Minkowski spacetime revisited.- Conclusions.- Problems.- Solutions to selected problems.- References.- Index.
£22.99
Springer International Publishing AG Superconcentration and Related Topics
Book SynopsisA certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple valleys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach.Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012.The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability.Table of ContentsPreface.- 1.Introduction.- 2.Markov semigroups.- 3.Super concentration and chaos.- 4.Multiple valleys.- 5.Talagrand’s method for proving super concentration.- 6.The spectral method for proving super concentration.- 7.Independent flips.- 8.Extremal fields.- 9.Further applications of hypercontractivity.- 10.The interpolation method for proving chaos.- 11.Variance lower bounds.- 12.Dimensions of level sets.- Appendix A. Gaussian random variables.- Appendix B. Hypercontractivity.- Bibliography.- Indices.
£67.49
Birkhauser Verlag AG Space-Time Algebra
Book SynopsisThis small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future.At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible.There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout ‘Space-Time Algebra’, despite its short length, and some of them are effectively still research topics for the future.From the Foreward by Anthony LasenbyTable of ContentsPreface to the Second Edition.- Introduction.- Part I:Geometric Algebra.- 1.Intrepretation of Clifford Algebra.- 2.Definition of Clifford Algebra.- 3.Inner and Outer Products.- 4.Structure of Clifford Algebra.- 5.Reversion, Scalar Product.- 6.The Algebra of Space.- 7.The Algebra of Space-Time.- Part II:Electrodynamics.- 8.Maxwell's Equation.- 9.Stress-Energy Vectors.- 10.Invariants .- 11. Free Fields.- Part III:Dirac Fields.- 12.Spinors.- 13.Dirac's Equation.- 14.Conserved Currents.- 15.C, P, T.- Part IV:Lorentz Transformations.- 16.Reflections and Rotations.- 17.Coordinate Transformations.- 18.Timelike Rotations.- 19.Scalar Product.- Part V:Geometric Calculus.- 20.Differentiation.- 21.Coordinate Transformations.- 22.Integration.- 23.Global and Local Relativity.- 24.Gauge Transformation and Spinor Derivatives.- Conclusion.- Appendices.- A.Bases and Pseudoscalars.- B.Some Theorems.- C.Composition of Spacial Rotations.- D.Matrix Representation of the Pauli Algebra.
£79.99
