The Geometry of Physics: An Introduction (Google eBook)

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Cambridge University Press, Nov 3, 2011 - Mathematics - 694 pages
2 Reviews
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 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. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
  

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Review: The Geometry of Physics: An Introduction

User Review  - 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 ... Read full review

Review: The Geometry of Physics: An Introduction

User Review  - Dave - Goodreads

I really like the exposition in this book. Read full review

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Contents

Preface to the Third Edition page
xix
1
5
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
R3 and Minkowski Space
191
11
529
22
535
26
541
48
547
60
553
6a Instantons
559
Forms and Homotopy Groups
583
Homotopies and Extensions
591

The Geometry of Surfaces in
201
8
215
Gausss Theorema Egregium
228
6b The Intrinsic Derivative and the Geodesic Equation
234
Geodesics
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
Fiber Bundles GaussBonnet and Topological Quantization
451
Connections and Associated Bundles
476
The Dirac Equation
491
YangMills Fields
523
2a Homotopy
602
Appendix A Forms in Continuum Mechanics
617
A f Concluding Remarks
627
Laplacians and Harmonic Cochains
633
Symmetries Quarks and Meson Masses
640
e A Reduced Symmetry Group
648
e The Symmetric Traceless 3 3 Matrices Are Irreducible
658
E b Application of Botts Extension of Morse Theory
665
References
671
561
675
191
677
451
679
583
681
221
684
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About the author (2011)

Theodore Frankel received his PhD from the University of California, Berkeley. He is currently Emeritus Professor of Mathematics at the University of California, San Diego.

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