Group Theory in Physics

An Introduction to Symmetry Principles, Group Representations, and Special Functions in Classical and Quantum Physics

Wu-Ki Tung

• Publisher: WSPC
• Year: 1985
• eBook ISBN: 9789813104044
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems.

Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry.

Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained.

A set of problems and solutions has been published in a separate booklet.

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Table of contents

• CONTENTS
• PREFACE
• To Beatrice, Bruce, and Lei
• Group Theory in Physics
• CHAPTER 1 INTRODUCTION Symmetry, Quantum Mechanics, Group Theory, and Special Functions in a Nutshell
• CHAPTER 2 BASIC GROUP THEORY
• CHAPTER 3 GROUP REPRESENTATIONS
• CHAPTER 4 GENERAL PROPERTIES OF IRREDUCIBEL VECTSORS AND OPERTORS
• CHAPTER 5 REPRESENTATIONS OF THE SYMMETRIC GROUPS
• CHAPTER 6 ONE-DIMENSIONAL CONTINUOUS GROUPS
• CHAPTER 7 ROTATIONS IN 3-DIMENSIONAL SPACE—THE GROUP SO(3)
• CHAPTER 8 THE GROUP SU(2) AND MORE ABOUT SO(3)
• CHAPTER 9 EUCLIDEAN GROUPS IN TWO- AND THREE-DIMENSIONAL SPACE
• CHAPTER 10 THE LORENTZ AND POINCARÉ GROUPS, AND SPACE-TIME SYMMETRIES
• CHAPTER 11 SPACE INVERSION INVARIANCE
• CHAPTER 12 TIME REVERSAL INVARIANCE
• CHAPTER 13 FINITE-DIMENSIONAL REPRESENTATIONS OF THE CLASSICAL GROUPS
• APPENDIX I NOTATIONS AND SYMBOLS
• APPENDIX II SUMMARY OF LINEAR VECTOR SPACES
• APPENDIX III GROUP ALGEBRA AND THE REDUCTION OF REGULAR REPRESENTATION
• APPENDIX IV SUPPLEMENTS TO THE THEORY OF SYMMETRIC GROUPS Sn
• APPENDIX V CLEBSCH-GORDAN COEFFICIENTS AND SPHERICAL HARMONICS
• APPENDIX VI ROTATIONAL AND LORENTZ SPINORS
• APPENDIX VII UNITARY REPRESENTATIONS OF THE PROPER LORENTZ GROUP
• APPENDIX VIII ANTI-LINEAR OPERATORS
• REFERENCES AND BIBLIOGRAPHY
• INDEX