The geometry of physics

An introduction

Theodore Frankel

694 pages, parution le 23/07/2004 (2^eme édition)

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Résumé

This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, elasticity theory, the geometry and topology of Kirchhoff's electric circuit laws, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers, quarks, and the quark model for mesons. Before a discussion of abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students.

This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self-study.

This second edition includes three new appendices, Appendix C, Symmetries, Quarks, and Meson Masses (which concludes with the famous Gell-Mann/Okubo mass formula); Appendix D, Representations and Hyperelastic Bodies; and Appendix E, Orbits and Morse-Bott Theory in Compact Lie Groups. Both Appendices C and D involve results from the theory of representations of compact Lie groups, which are developed here. Appendix E delves deeper into the geometry and topology of compact Lie groups.

Sommaire

Manifolds, Tensors and Exterior Forms
- Manifolds and vector fields
- Tensors and exterior forms
- Integration of differential forms
- The Lie derivative
- The Poincaré lemma and potentials
- Holonomic and non-holonomic constraints
Geometry and Topology
- R3 and Minkowski space
- The geometry of surfaces in R3
- Covariant differentiation and curvature
- Geodesics
- Relativity, tensors, and curvature
- Curvature and topology: Synge's theorem
- Betti numbers and de Rham's theorem
- Harmonic forms
Lie Groups, Bundles and Chern Forms
- Lie groups
- Vector bundles in geometry and physics
- Fiber bundles, Gauss-Bonnet, and topological quantization
- Connections and associated bundles
- The Dirac equation
- Yang-Mills fields
- Betti numbers and covering spaces
- Chern forms and homotopy groups

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Theodore Frankel
Parution	23/07/2004
Édition	2^eme édition
Nb. de pages	694
Format	17,5 x 25,5
Couverture	Broché
Poids	1240g
Intérieur	Noir et Blanc
EAN13	9780521539272
ISBN13	978-0-521-53927-2