The geometry of physics

An introduction

Theodore Frankel

690 pages, parution le 01/01/1999

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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, 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. 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 also be of interest 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.

Contents

Part I. 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

Part II. 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

Part III. 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

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Theodore Frankel
Parution	01/01/1999
Nb. de pages	690
Format	17,8 x 25,5
Couverture	Broché
Poids	1228g
Intérieur	Noir et Blanc
EAN13	9780521387538