Group Theory & General Relativity

Representations of the Lorentz Group and Their Applications to the Gravitational Field

Moshe Carmeli

• Publisher: ICP
• Year: 2000
• ISBN:
  9781848160187
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -particularly the Lorentz and the SL(2,C) groups — to the theory of general relativity. Each chapter is concluded with a set of problems.The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2,C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.

Table of contents

• CONTENTS
• INTRODUCTION
• CHAPTER ONE THE ROTATION GROUP
• CHAPTER TWO THE LORENTZ GROUP
• CHAPTER THREE SPINOR REPRESENTATION OF THE LORENTZ GROUP
• CHAPTER FOUR PRINCIPAL SERIES OF REPRESENTATIONS OF SL(2, C)
• CHAPTER FIVE COMPLEMENTARY SERIES OF REPRESENTATIONS OF SL(2, C)
• CHAPTER SIX COMPLETE SERIES OF REPRESENTATIONS OF SL(2, C)
• CHAPTER SEVEN ELEMENTS OF GENERAL RELATIVITY THEORY
• CHAPTER EIGHT SPINORS IN GENERAL RELATIVITY
• CHAPTER NINE SL(2, C) GAUGE THEORY OF THE GRAVITATIONAL FIELD: THE NEWMAN–PENROSE EQUATIONS
• CHAPTER TEN ANALYSIS OF THE GRAVITATIONAL FIELD
• CHAPTER ELEVEN SOME EXACT SOLUTIONS OF THE GRAVITATIONAL FIELD EQUATIONS
• CHAPTER TWELVE THE BONDI–METZNER–SACHS GROUP
• APPENDIX A REVIEW OF GROUP THEORY
• APPENDIX B BASIC CONCEPTS OF REPRESENTATIONS THEORY
• APPENDIX C INFINITE-DIMENSIONAL REPRESENTATIONS
• APPENDIX D GRAVITATIONAL FIELD EQUATIONS
• APPENDIX E TRANSFORMATION PROPERTIES OF THENEWMAN–PENROSE FIELD VARIABLES
• BIBLIOGRAPHY
• INDEX