The Geometry of Physics

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  • Edition: 3rd
  • Format: Paperback
  • Copyright: 2011-12-26
  • Publisher: Cambridge Univ Pr
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Supplemental Materials

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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 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.

Table of Contents

Preface to the Third Edition
Preface to the Second Edition
Preface to the revised printing
Preface to the First Edition
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 nonholonomic constraints
Geometry and Topology
R3 and Minkowski space
The geometry of surfaces in R3
Covariant differentiation and curvature
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
Forms in continuum mechanics
Harmonic chains and Kirchhoff's circuit laws
Symmetries, quarks, and Meson masses
Representations and hyperelastic bodies
Orbits and Morse-Bott theory in compact Lie groups
Table of Contents provided by Publisher. All Rights Reserved.

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