The Geometry of Physics

An Introduction

Theodore Frankel

• Publisher: Cambridge University Press
• Year: 2011
• Print ISBN: 9781107602601
• eBook ISBN: 9781139154147
• Edition: 3
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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

• Cover
• The Geometry of Physics
• Title
• Copyright
• ForThom-kat, Mont, Dave and Jonnie and In fond memory of Raoul Bott 1923–2005
• Contents
• Preface to the Third Edition
• Preface to the Second Edition
• Preface to the Revised Printing
• Preface to the First Edition
• OVERVIEW:An Informal Overview of Cartan’s Exterior Differential Forms, Illustrated with an Application to Cauchy’s Stress Tensor
• PART ONE
• CHAPTER 1
• CHAPTER 2
• CHAPTER 3
• CHAPTER 4
• CHAPTER 5
• CHAPTER 6
• PART TWO
• CHAPTER 7
• CHAPTER 8
• CHAPTER 9
• CHAPTER 10
• CHAPTER 11
• CHAPTER 12
• CHAPTER 13
• CHAPTER 14
• PART THREE
• CHAPTER 15
• CHAPTER 16
• CHAPTER 17
• CHAPTER 18
• CHAPTER 19
• CHAPTER 20
• CHAPTER 21
• CHAPTER 22
• APPENDIX A
• APPENDIX B
• APPENDIX C
• APPENDIX D
• APPENDIX E
• References
• Index