Symmetry

An Introduction to Group Theory and Its Applications

R. McWeeny, H. Jones

• Publisher: Pergamon
• Year: 2013
• ISBN:
  9781483226248
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.

Table of contents

• Front Cover
• Symmetry: An Introduction to Group Theory and its Applications
• Copyright Page
• Table of Contents
• THE INTERNATIONAL ENCYCLOPEDIA OF PHYSICAL CHEMISTRY AND CHEMICAL PHYSICS
• INTRODUCTION
• PREFACE
• CHAPTER 1. GROUPS
• CHAPTER 2. LATTICES AND VECTOR SPACES
• CHAPTER 3. POINT AND SPACE GROUPS
• CHAPTER 4. REPRESENTATIONS OF POINT AND TRANSLATION GROUPS
• CHAPTER 5. IRREDUCIBLE REPRESENTATIONS
• CHAPTER 6. APPLICATIONS INVOLVING ALGEBRAIC FORMS
• CHAPTER 7. APPLICATIONS INVOLVING FUNCTIONS AND OPERATORS
• CHAPTER 8. APPLICATIONS INVOLVING TENSORS AND TENSOR OPERATORS
• APPENDIX 1: Representations carried by harmonic functions
• APPENDIX 2: Alternative bases for cubic groups
• INDEX