Applications of Finite Groups

J. S. Lomont

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9781483231327
• eBook ISBN: 9781483268965
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

Table of contents

• Front Cover
• Applications of Finite Groups
• Copyright Page
• Table of Contents
• Preface
• List of Symbols
• Chapter I. MATRICES
• Chapter II. GROUPS
• Chapter III. REPRESENTATIONS
• Chapter IV. APPLICATIONS
• Chapter V. SUBGROUPS AND REPRESENTATIONS
• Chapter VI. SPACE GROUP REPRESENTATIONS AND ENERGY BANDS
• Chapter VII. SYMMETRIC GROUPS
• Chapter VIII. APPLICATIONS
• References
• Appendix I: Proof of the Key Theorem of Representation Theory
• Appendix II: Irreducible Representations of D3, D4, D6, T, O, and ϕ
• Appendix III: The Lorentz Groups
• Subject Index