Physics On Manifolds
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Analysis Manifolds And Physics Revised Edition
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Author : Yvonne Choquet-Bruhat
language : en
Publisher: Gulf Professional Publishing
Release Date : 1982
Analysis Manifolds And Physics Revised Edition written by Yvonne Choquet-Bruhat and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
Differential Manifolds And Theoretical Physics
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Author :
language : en
Publisher: Academic Press
Release Date : 1985-05-24
Differential Manifolds And Theoretical Physics written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-05-24 with Mathematics categories.
Differential Manifolds and Theoretical Physics
Tensors And Manifolds
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Author : Robert Wasserman
language : en
Publisher: Oxford University Press, USA
Release Date : 2004
Tensors And Manifolds written by Robert Wasserman and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Language Arts & Disciplines categories.
This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.
Physics On Manifolds
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Author : M. Flato
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Physics On Manifolds written by M. Flato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris. Its title accurately reflects the domains to which Yvonne Choquet-Bruhat has made essential contributions. Since the rise of General Relativity, the geometry of Manifolds has become a non-trivial part of space-time physics. At the same time, Functional Analysis has been of enormous importance in Quantum Mechanics, and Quantum Field Theory. Its role becomes decisive when one considers the global behaviour of solutions of differential systems on manifolds. In this sense, General Relativity is an exceptional theory in which the solutions of a highly non-linear system of partial differential equations define by themselves the very manifold on which they are supposed to exist. This is why a solution of Einstein's equations cannot be physically interpreted before its global behaviour is known, taking into account the entire hypothetical underlying manifold. In her youth, Yvonne Choquet-Bruhat contributed in a spectacular way to this domain stretching between physics and mathematics, when she gave the proof of the existence of solutions to Einstein's equations on differential manifolds of a quite general type. The methods she created have been worked out by the French school of mathematics, principally by Jean Leray. Her first proof of the local existence and uniqueness of solutions of Einstein's equations inspired Jean Leray's theory of general hyperbolic systems.
Differential Equations On Manifolds And Mathematical Physics
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Author : Vladimir M. Manuilov
language : en
Publisher: Springer Nature
Release Date : 2022-01-21
Differential Equations On Manifolds And Mathematical Physics written by Vladimir M. Manuilov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-21 with Mathematics categories.
This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.
Analysis Manifolds And Physics Part Ii Revised And Enlarged Edition
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Author : Y. Choquet-Bruhat
language : en
Publisher: Elsevier
Release Date : 2000-11-08
Analysis Manifolds And Physics Part Ii Revised And Enlarged Edition written by Y. Choquet-Bruhat and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-08 with Science categories.
Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.
Differential Geometry And Mathematical Physics
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Author : Gerd Rudolph
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09
Differential Geometry And Mathematical Physics written by Gerd Rudolph and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-09 with Science categories.
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Differential Manifolds
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Author : Paul Baillon
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-11-22
Differential Manifolds written by Paul Baillon and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Science categories.
Differential Manifold is the framework of particle physics and astrophysics nowadays. It is important for all research physicists to be well accustomed to it and even experimental physicists should be able to manipulate equations and expressions in that framework. This book gives a comprehensive description of the basics of differential manifold with a full proof of any element. A large part of the book is devoted to the basic mathematical concepts in which all necessary for the development of the differential manifold is expounded and fully proved. This book is self-consistent: it starts from first principles. The mathematical framework is the set theory with its axioms and its formal logic. No special knowledge is needed.
Smooth Manifolds And Fibre Bundles With Applications To Theoretical Physics
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Author : Steinar Johannesen
language : en
Publisher: CRC Press
Release Date : 2016-12-08
Smooth Manifolds And Fibre Bundles With Applications To Theoretical Physics written by Steinar Johannesen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Mathematics categories.
This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, this book provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.
Analysis Manifolds And Physics
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Author : Yvonne Choquet-Bruhat
language : en
Publisher: Elsevier Science & Technology
Release Date : 1989
Analysis Manifolds And Physics written by Yvonne Choquet-Bruhat and has been published by Elsevier Science & Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This second, companion volume contains 92 applications developing concepts and theorems presented or mentioned in the first volume. Introductions to and applications in several areas not previously covered are also included such as graded algebras with applications to Clifford algebras and (S)pin groups, Weyl Spinors, Majorana pinors, homotopy, supersmooth mappings and Berezin integration, Noether's theorems, homogeneous spaces with applications to Stiefel and Grassmann manifolds, cohomology with applications to (S)pin structures, Bauml;cklund transformations, Poisson manifolds, conformal transformations, Kaluza-Klein theories, Calabi-Yau spaces, universal bundles, bundle reduction and symmetry breaking, Euler-Poincareacute; characteristics, Chern-Simons classes, anomalies, Sobolev embedding, Sobolev inequalities, Wightman distributions and Schwinger functions.The material included covers an unusually broad area and the choice of problems is guided by recent applications of differential geometry to fundamental problems of physics as well as by the authors' personal interests. Many mathematical tools of interest to physicists are presented in a self-contained manner, or are complementary to material already presented in part I. All the applications are presented in the form of problems with solutions in order to stress the questions the authors wished to answer and the fundamental ideas underlying applications. The answers to the solutions are explicitly worked out, with the rigor necessary for a correct usage of the concepts and theorems used in the book. This approach also makes part I accessible to a much larger audience.The book has been enriched by contributions from Charles Doering, Harold Grosse, B. Kent Harrison, N.H. Ibragimov and Carlos Moreno, and collaborations with Ioannis Bakas, Steven Carlip, Gary Hamrick, Humberto La Roche and Gary Sammelmann.