Mathematical / Computational / Theoretical physics Books

Book Synopsis1. Introduction and Summary.- 2. Dynamics and Work.- 3. Information Entropy.- 3.a Entropy and relative entropy.- 3.b Gibbs states.- 3.c Entropy-increasing processes.- 4. Heat Baths.- 5. Reversible Processes.- 6. Closed Finite Systems.- 6.a Available work.- 6.b Recurrences.- 6.c Entropy functions.- 7. Open Systems.- 7.a Markov description.- 7.b Available work and entropy.- 7.c Master equation models.- 8. External Perturbations.- 8.a Models of the perturbations.- 8.b Classical systems.- 8.c Quantum systems.- 8.d Effects on the entropy functions.- 9. Thermodynamic Limit.- 10. Thermodynamic Entropy.- 10.a Thermodynamic processes and entropy.- 10.b Properties of the entropy functions.- 10.c Irreversibility and approach to equilibrium.- 11. Measurements, Entropy and Work.- 11.a Observations on the system.- 11.b Information and entropy.- 11.c Exchange of work and heat.- 12. Other Approaches.- Appendix A. Quantum Markov Processes.- A.1 Reduced dynamics.- A.2 Markov processes.- A.3 Non-passivitTable of Contents1. Introduction and Summary.- 2. Dynamics and Work.- 3. Information Entropy.- 3.a Entropy and relative entropy.- 3.b Gibbs states.- 3.c Entropy-increasing processes.- 4. Heat Baths.- 5. Reversible Processes.- 6. Closed Finite Systems.- 6.a Available work.- 6.b Recurrences.- 6.c Entropy functions.- 7. Open Systems.- 7.a Markov description.- 7.b Available work and entropy.- 7.c Master equation models.- 8. External Perturbations.- 8.a Models of the perturbations.- 8.b Classical systems.- 8.c Quantum systems.- 8.d Effects on the entropy functions.- 9. Thermodynamic Limit.- 10. Thermodynamic Entropy.- 10.a Thermodynamic processes and entropy.- 10.b Properties of the entropy functions.- 10.c Irreversibility and approach to equilibrium.- 11. Measurements, Entropy and Work.- 11.a Observations on the system.- 11.b Information and entropy.- 11.c Exchange of work and heat.- 12. Other Approaches.- Appendix A. Quantum Markov Processes.- A.1 Reduced dynamics.- A.2 Markov processes.- A.3 Non-passivity of Markov processes.- A.4 Non-KMS property of Markov processes.- A.5 Quantum thermal fluctuations.- Appendix B. Sensitivity of Hyperbolic Motion.- References.- Notation Index.

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Book SynopsisFirst published in Latin in 1687, Mathematical Principles of Natural Philosophy, commonly referred to as The Principia, is the groundbreaking work of science and mathematics by Isaac Newton. Consisting of three books, The Principia was updated twice by Newton during his lifetime, with new editions published in 1713 and 1726, as he further refined and expanded his ideas. The Principia introduced Newton''s laws of motion and his law of universal gravitation that explained the motion of all the bodies in the solar system, an area of science that had previously been incomplete and poorly understood. Newton''s seminal work established the foundation for classical mechanics and is considered one of the most important and influential scientific books ever published. The theories and formulas created and explained in The Principia comprised the basis for a new field of mathematics now known as calculus. While some of his contemporaries were reluctant to accept Newton''s ideas, by the end of

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Book SynopsisThis book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations.Trade ReviewFrom the reviews: "This book provides comprehensive coverage of the major aspects of the DG-FEM, from derivation, analysis and implementation of the method to simulation of application problems. It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics and engineering." -Mathematical Reviews "The book under review presents basic ideas, theoretical analysis, MATLAB implementation and applications of the DG-FEM. … The representative references quoted are useful for any reader interested in applying the method in a particular area. … This book provides comprehensive coverage of the major aspects of the DG-FEM … . It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics, and engineering." (Weimin Han, Mathematical Reviews, Issue 2008 k) "This book is intended to offer a comprehensive introduction to, and an efficient implementation of discontinuous Galerkin finite element methods … . Each chapter of the book is largely self-contained and is complemented by adequate exercises. … The style of writing is clear and concise … . is an exceptionally complete and accessible reference for graduate students, researchers, and professionals in applied mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference." (Marius Ghergu, Zentralblatt MATH, Vol. 1134 (12), 2008)Table of ContentsThe key ideas.- Making it work in one dimension.- Insight through theory.- Nonlinear problems.- Beyond one dimension.- Higher-order equations.- Spectral properties of discontinuous Galerkin operators.- Curvilinear elements and nonconforming discretizations.- Into the third dimension.

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Book SynopsisI Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem.- Appendix 9 Poincaré's geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.Trade ReviewSecond Edition V.I. Arnol’d Mathematical Methods of Classical Mechanics "The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview." —AMERICAN MATHEMATICAL MONTHLYTable of ContentsI Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov’s theorem.- Appendix 9 Poincaré’s geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.

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Book SynopsisI. Basic Properties of Particles and Fields.- 1. Electromagnetism.- 2. Interaction of Fields and Particles.- 3. Dynamics of Classical Fields.- 4. Solitons.- 5. Path Integrals and Instantons.- II. Basic Principles and Applications of Differential Geometry.- 6. Differentiable Manifolds?Tensor Analysis.- 7. Differential Forms and the Exterior Calculus.- 8. Integral Calculus on Manifolds.- 9. Dirac Monopoles.- 10. Smooth Maps?Winding Numbers.- 11. Symmetries and Conservation Laws.Trade ReviewFROM THE REVIEWS: MATHEMATICAL REVIEWS"It is particularly well-suited as an introductory text, since the author takes great care to anticipate points that may cause confusion…The author does a good job of focusing on the fundamentals…[The first] part of the book works as either a self-contained introduction to classical field theory, or as a complement to a good text on classical electrodynamics…[The second] part of the book is very clear and well planned…works as a self-contained introduction to manifolds and differential forms, or, even better, as a compliment to a concise mathematics text.” PHYSICS TODAY"The present volume is a welcome edition to the growing number of books that develop geometrical language and use it to describe new developments in particle physics ... It provides clear treatment that is accessible to graduate students with a knowledge of advanced calculus and of classical physics.... The second half of the book deals with the principles of differential geometry and its applications, with a mathematical machinery of very wide range. Here clear line drawings and illustrations supplement the multitude of mathematical definitions. This section, in its clarity and pedagogy, is reminiscent of Gravitation by Charles Misner, Kip Thorne and John Wheeler.... Felsager gives a very clear presentation of the use of geometric methods in particle physics.... For those who have resisted learning this new language, his book provides a very good introduction as well as physical motivation. The inclusion of numerous exercises, worked out, renders the book useful for independent study also. I hope this book will be followed by others from authors with equal flair to provide a readable excursion into the next step." Table of ContentsPart I: Basic Properties of Particles and Fields; 1. Electromagnetism; 2. Interaction of Fields and Particles; 3. Dynamics of Classical Fields; 4. Solitons; 5. Path-Integrals and Instantons; Part II: Basic Principles and Applications of Differential Geometry; 6. Differentiable Manifolds-Tensor Analysis; 7. Differential Forms and the Exterior Algebra; 8. Integral Calculus on Manifolds; 9. Dirac Monopoles; 10. Smooth Maps-Winding Numbers; 11. Symmetries and Conservation Laws

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Book Synopsis1. Introduction.- 1.1. Order Symbols, Uniformity.- 1.2. Asymptotic Expansion of a Given Function.- 1.3. Regular Expansions for Ordinary and Partial Differential Equations.- References.- 2. Limit Process Expansions for Ordinary Differential Equations.- 2.1. The Linear Oscillator.- 2.2. Linear Singular Perturbation Problems with Variable Coefficients.- 2.3. Model Nonlinear Example for Singular Perturbations.- 2.4. Singular Boundary Problems.- 2.5. Higher-Order Example: Beam String.- References.- 3. Limit Process Expansions for Partial Differential Equations.- 3.1. Limit Process Expansions for Second-Order Partial Differential Equations.- 3.2. Boundary-Layer Theory in Viscous, Incompressible Flow.- 3.3. Singular Boundary Problems.- References.- 4. The Method of Multiple Scales for Ordinary Differential Equations.- 4.1. Method of Strained Coordinates for Periodic Solutions.- 4.2. Two Scale Expansions for the Weakly Nonlinear Autonomous Oscillator.- 4.3. Multiple-Scale Expansions for General Weakly Nonlinear Oscillators.- 4.4. Two-Scale Expansions for Strictly Nonlinear Oscillators.- 4.5. Multiple-Scale Expansions for Systems of First-Order Equations in Standard Form.- References.- 5. Near-Identity Averaging Transformations: Transient and Sustained Resonance.- 5.1. General Systems in Standard Form: Nonresonant Solutions.- 5.2. Hamiltonian System in Standard Form; Nonresonant Solutions.- 5.3. Order Reduction and Global Adiabatic Invariants for Solutions in Resonance.- 5.4. Prescribed Frequency Variations, Transient Resonance.- 5.5. Frequencies that Depend on the Actions, Transient or Sustained Resonance.- References.- 6. Multiple-Scale Expansions for Partial Differential Equations.- 6.1. Nearly Periodic Waves.- 6.2. Weakly Nonlinear Conservation Laws.- 6.3. Multiple-Scale Homogenization.- References.Table of Contents1. Introduction.- 1.1. Order Symbols, Uniformity.- 1.2. Asymptotic Expansion of a Given Function.- 1.3. Regular Expansions for Ordinary and Partial Differential Equations.- References.- 2. Limit Process Expansions for Ordinary Differential Equations.- 2.1. The Linear Oscillator.- 2.2. Linear Singular Perturbation Problems with Variable Coefficients.- 2.3. Model Nonlinear Example for Singular Perturbations.- 2.4. Singular Boundary Problems.- 2.5. Higher-Order Example: Beam String.- References.- 3. Limit Process Expansions for Partial Differential Equations.- 3.1. Limit Process Expansions for Second-Order Partial Differential Equations.- 3.2. Boundary-Layer Theory in Viscous, Incompressible Flow.- 3.3. Singular Boundary Problems.- References.- 4. The Method of Multiple Scales for Ordinary Differential Equations.- 4.1. Method of Strained Coordinates for Periodic Solutions.- 4.2. Two Scale Expansions for the Weakly Nonlinear Autonomous Oscillator.- 4.3. Multiple-Scale Expansions for General Weakly Nonlinear Oscillators.- 4.4. Two-Scale Expansions for Strictly Nonlinear Oscillators.- 4.5. Multiple-Scale Expansions for Systems of First-Order Equations in Standard Form.- References.- 5. Near-Identity Averaging Transformations: Transient and Sustained Resonance.- 5.1. General Systems in Standard Form: Nonresonant Solutions.- 5.2. Hamiltonian System in Standard Form; Nonresonant Solutions.- 5.3. Order Reduction and Global Adiabatic Invariants for Solutions in Resonance.- 5.4. Prescribed Frequency Variations, Transient Resonance.- 5.5. Frequencies that Depend on the Actions, Transient or Sustained Resonance.- References.- 6. Multiple-Scale Expansions for Partial Differential Equations.- 6.1. Nearly Periodic Waves.- 6.2. Weakly Nonlinear Conservation Laws.- 6.3. Multiple-Scale Homogenization.- References.

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Book Synopsis1. Hilbert Space.- 2. Spinors.- Finite Number of Dimensions.- 3. Rotations in n Dimensions.- 4. Null Vectors and Null Planes.- 5. The Independence Theorem.- 6. Specification of a Null Plane without Its Coordinates.- 7. Matrix Notation.- 8. Expression of a Rotation in Terms of an Infinitesimal Rotation.- 9. Complex Rotations.- 10. The Noncommutative Algebra.- 11. Rotation Operators.- 12. Fixation of the Coefficients of Rotation Operators.- 13. The Ambiguity of Sign.- 14. Kets and Bras.- 15. Simple Kets.- Even Number of Dimensions.- 16. The Ket Matrix.- 17. The Two-Ket-Matrix Theorem.- 18. The Connection between Two Ket Matrices.- 19. The Representation of Kets.- 20. The Representative of a Simple Ket. General.- 21. The Representative of a Simple Ket. Special Cases.- 22. Fixation of the Coefficients of Simple Kets.- 23. The Scalar Product Formula.- Infinite Number of Dimensions.- 24. The Need for Bounded Matrices.- 25. The Infinite Ket Matrix.- 26. Passage from One Ket Matrix to Another.Table of Contents1. Hilbert Space.- 2. Spinors.- Finite Number of Dimensions.- 3. Rotations in n Dimensions.- 4. Null Vectors and Null Planes.- 5. The Independence Theorem.- 6. Specification of a Null Plane without Its Coordinates.- 7. Matrix Notation.- 8. Expression of a Rotation in Terms of an Infinitesimal Rotation.- 9. Complex Rotations.- 10. The Noncommutative Algebra.- 11. Rotation Operators.- 12. Fixation of the Coefficients of Rotation Operators.- 13. The Ambiguity of Sign.- 14. Kets and Bras.- 15. Simple Kets.- Even Number of Dimensions.- 16. The Ket Matrix.- 17. The Two-Ket-Matrix Theorem.- 18. The Connection between Two Ket Matrices.- 19. The Representation of Kets.- 20. The Representative of a Simple Ket. General.- 21. The Representative of a Simple Ket. Special Cases.- 22. Fixation of the Coefficients of Simple Kets.- 23. The Scalar Product Formula.- Infinite Number of Dimensions.- 24. The Need for Bounded Matrices.- 25. The Infinite Ket Matrix.- 26. Passage from One Ket Matrix to Another.- 27. The Various Kinds of Ket Matrices.- 28. Failure of the Associative Law.- 29. The Fundamental Commutators.- 30. Boson Variables.- 31. Boson Emission and Absorption Operators.- 32. Infinite Determinants.- 33. Validity of the Scalar Product Formula.- 34. The Energy of a Boson.- 35. Physical Application.

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Table of Contents1. Basic definitions.- 2. The invariant bilinear form and the generalized Casimir operator.- 3. Integrable representations and the Weyl group of a Kac-Moody algebra.- 4. Some properties of generalized Cartan matrices.- 5. Real and imaginary roots.- 6. Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group.- 7. Affine Lie algebras: the realization (case k = 1).- 8. Affine Lie algebras: the realization (case k = 2 or 3). Application to the classification of finite order automorphisms.- 9. Highest weight modules over the Lie algebra g(A).- 10. Integrable highest weight modules: the character formula.- 11. Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem.- 12. Integrable highest weight modules over affine Lie algebras. Application to ?-function identities.- 13. Affine Lie algebras, theta functions and modular forms.- 14. The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations.- Index of notations and definitions.- References.

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Book SynopsisFor a physicist, "noise" is not just about sounds, but refers to any random physical process that blurs measurements, and in so doing stands in the way of scientific knowledge.This book deals with the most common types of noise, their properties, and some of their unexpected virtues. The text explains the most useful mathematical concepts related to noise. Finally, the book aims at making this subject more widely known and to stimulate the interest for its study in young physicists.Table of Contents Preface Acknowledgments Author biography Cosmic noise What is noise? Mathematical models of noise The science of Johnson noise Final remarks Further reading

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Book SynopsisThis is an introductory textbook on computational methods and techniques intended for undergraduates at the sophomore or junior level in the fields of science, mathematics, and engineering. It provides an introduction to programming languages such as FORTRAN 90/95/2000 and covers numerical techniques such as differentiation, integration, root finding, and data fitting. The textbook also entails the use of the Linux/Unix operating system and other relevant software such as plotting programs, text editors, and mark up languages such as LaTeX. It includes multiple homework assignments.Table of Contents Preface Acknowledgments Author biographies 1. The Linux/Unix operating system 2. Text editors 3. The Fortran 90 programming language 4. Numerical techniques 5. Problem solving methodologies 6. Worksheet assignments 7. Homework assignments Appendices

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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.

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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.

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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.

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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.

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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.

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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

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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.

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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

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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.

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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.

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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.

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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.

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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.

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Book Synopsis​This 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.

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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.

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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).

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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).

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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.

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