Cornwell J.F. Group theory in physics. An introduction

San Diego: Academic Press. – 1997. – 359 p. No longer do physicists regard group theory merely as providing a valuable tool for the elucidation of the symmetry aspects of physical problems. Recent developments, particularly in high-energy physics, have transformed its role so that it now occupies a crucial and central position. Group Theory in Physics - An Introduction is an abridgement and revision of Volumes I and II of the author’s previous three volume work Group Theory in Physics. It has been designed to provide a succinct introduction to the subject for advanced undergraduate and postgraduate students, and for others approaching the subject for the first time. It aims to present all the relevant important mathematical developments in a form that is easy for physicists to understand and appreciate. The treatment starts with the basic concepts and is carried through to some of the most significant developments in atomic physics, electronic energy bands in solids and the theory of elementary particles. No prior knowledge of group theory is assumed, and for convenience, various relevant algebraic concepts are summarised in appendices. The intention has been to concentrate on introducing and describing in detail the most important basic ideas and the role that they play in physical problems. Nevertheless, the mathematical coverage goes outside the strict confines of group theory itself and includes a study of Lie algebras, which, though related to Lie groups, are often developed by mathematicians as a separate subject. For the benefit of readers who may wish to concentrate on specific applications, the following list gives the relevant chapters:
electronic energy bands in solids: Chapters 1, 2, and 4 to 7;
atomic physics: Chapters 1 to 6, and 8 to 10;
elementary particles: Chapters 1 to 6, and 8 to 13.The Basic Framework
The Structure of Groups
Lie Groups
Representations of Groups - Principal Ideas
Representations of Groups - Developments
Group Theory in Quantum Mechanical Calculations
Crystallographic Space Groups
The Role of Lie Algebras
The Relationships between Lie Groups and Lie Algebras Explored
The Three-dimensional Rotation Groups
The Structure of Semi-simple Lie Algebras
Representations of Semi-simple Lie Algebras
Symmetry schemes for the elementary particles
Matrices
Vector Spaces
Character Tables for the Crystallographic Point Groups
Properties of the Classical Simple Complex Lie Algebras