The Geometry of Physics: An Introduction

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Cambridge University Press, 2004 - Всего страниц: 694
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This book provides 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, the deformation tensors of elasticity, 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 quark model for mesons. Before discussing 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. Ideal for graduate and advanced undergraduate students of physics, engineering and mathematics as a course text or for self study.
  

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Review: The Geometry of Physics: An Introduction

Пользовательский отзыв  - Toby Bartels - Goodreads

If you wish to apply geometry to physics, then you must read this book. There is no alternative. This is the material that matters —any other approach is deficient. There is no better exposition than ... Читать весь отзыв

Review: The Geometry of Physics: An Introduction

Пользовательский отзыв  - Dave - Goodreads

I really like the exposition in this book. Читать весь отзыв

Содержание

Manifolds and Vector Fields
3
Tensors and Exterior Forms
37
Integration of Differential Forms
95
The Lie Derivative
125
The Poincare Lemma and Potentials
155
Holonomic and Nonholonomic Constraints
165
K3 and Minkowski Space
191
The Geometry of Surfaces in R3
201
Fiber Bundles GaussBonnet and Topological Quantization
451
Connections and Associated Bundles
475
The Dirac Equation
491
YangMills Fields
523
Betti Numbers and Covering Spaces
561
Chern Forms and Homotopy Groups
583
Appendix A Forms in Continuum Mechanics
617
A e Stored Energy of Deformation
623

Covariant Differentiation and Curvature
241
Geodesies
269
Relativity Tensors and Curvature
291
Synges Theorem
323
Betti Numbers and De Rhams Theorem
333
Harmonic Forms
361
Lie Groups
391
Vector Bundles in Geometry and Physics
413
A g Some Typical Computations Using Forms
629
A h Concluding Remarks
635
Symmetries Quarks and Meson Masses
648
e A Reduced Symmetry Group
656
Appendix E Orbits and MorseBott Theory in Compact Lie Groups
670
Index
683
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Об авторе (2004)

Frankel received his Ph.D. from the University of California, Berkeley. He is currently emeritus professor of mathematics at the University of California, San Diego.

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