Differential Geometry And Lie Groups For Physicists
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Differential Geometry And Lie Groups For Physicists
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Author : Marián Fecko
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-12
Differential Geometry And Lie Groups For Physicists written by Marián Fecko and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-12 with Science categories.
Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.
Differential Geometry And Lie Groups For Physicists
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Author : Marián Fecko
language : en
Publisher:
Release Date : 2014-05-14
Differential Geometry And Lie Groups For Physicists written by Marián Fecko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Mathematics categories.
Advanced undergraduate and graduate 2006 textbook introducing differential geometry for theoretical physics and applied mathematics.
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.
Lie Groups Physics And Geometry
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Author : Robert Gilmore
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-17
Lie Groups Physics And Geometry written by Robert Gilmore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-17 with Science categories.
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
Modern Differential Geometry For Physicists
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Author : Chris J. Isham
language : en
Publisher: World Scientific
Release Date : 1999
Modern Differential Geometry For Physicists written by Chris J. Isham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
"The result is a book which provides a rapid initiation to the material in question with care and sufficient detail to allow the reader to emerge with a genuine familiarity with the foundations of these subjects".Mathematical Reviews"This book is carefully written, and attention is paid to rigor and relevant details The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism". Mathematical Reviews
Lie Groups Lie Algebras Cohomology And Some Applications In Physics
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Author : Josi A. de Azcárraga
language : en
Publisher: Cambridge University Press
Release Date : 1998-08-06
Lie Groups Lie Algebras Cohomology And Some Applications In Physics written by Josi A. de Azcárraga and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-06 with Mathematics categories.
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
Tensor Calculus And Differential Geometry For Engineers
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Author : Shahab Sahraee
language : en
Publisher: Springer Nature
Release Date : 2023-11-10
Tensor Calculus And Differential Geometry For Engineers written by Shahab Sahraee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-10 with Technology & Engineering categories.
The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.
Differential Geometric Foundations Of Non Equilibrium Thermodynamics
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Author : Marcus Hildebrandt
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-02-27
Differential Geometric Foundations Of Non Equilibrium Thermodynamics written by Marcus Hildebrandt and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-27 with Science categories.
While all field theories are nowadays available in a modern, differential geometric, coordinate free formulation on manifolds this has been so far only rudimentary accomplished in general non-equilibrium thermodynamics. In this work it is shown how a fitting geometric structure can be derived for arbitrary compact (discrete Schottky Systems) thermodynamic systems, such as stars and black holes, using only a few thermodynamic principles. This leads to deep geometric insights. Some central results are the following: while in the theory of relativity the energy-momentum tensor determines the geometry of the space, in non-equilibrium thermodynamics, the 1-form of the entropy production rate is responsible for the emergence of a well-known geometric structure: the contact geometry. Relaxation processes remain in the fibers in which they start and end on an attractor manifold, that can be identified with the classical equilibrium subspace of thermostatics. One then proves, that outside this attractor manifold there are no reversible process directions. As a consequence of this, the 2nd Law of thermodynamics lives mainly on the fibers of the state manifold, the so called vertical geometric structure, while the 1st Law of thermodynamics is formulated on the horizontal components of the state manifold. The internal energy provides a physical gauge for each fiber. The 1st and 2nd Law of thermodynamics are coupled via the representation of the entropy flux 1-form that can be represented in the dual basis of exchange 1-forms such as the heat 1-form. This fact can be used to provide a "coordinate free" ("invariant") definition of non-equilibrium temperature. Finally, it is shown that probably the most general geometric structure to model non-equilibrium thermodynamics of compact (discrete Schottky systems) systems is given by a composite fibred cocontact phase manifold that includes time as an explicit dimension.
Group Representations Ergodic Theory And Mathematical Physics
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Group Representations Ergodic Theory And Mathematical Physics written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.
Geometry Topology And Physics
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Geometry Topology And Physics written by Boris N. Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.