Symmetries in Physics Group Theory Applied to Physical Problems [Paperback]

Symmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.Symmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.1. Introduction.- 2. Elements of the Theory of Finite Groups.- 2.1 Symmetry and Group Concepts: A Basic Example.- 2.2 General Theorems on Group Theory.- 2.3 Conjugacy Classes.- 3. Discrete Symmetry Groups.- 3.1 Point Groups.- 3.1.1 Symmetry Elements.- 3.1.2 Proper Point Groups.- 3.1.3 Improper Point Groups.- 3.2 Colour Groups and Magnetic Groups.- 3.3 Double Groups.- 3.4 Lattices, the Translation Group and Space Group.- 3.4.1 Normal Space Groups.- 3.4.2 Colour and Magnetic Space Groups.- 3.4.3 Double Space Groups.- 3.5 Permutation Groups.- 3.6 Other Finite Groups.- 4. Representations of Finite Groups.- 4.1 Linear Spaces and Operators.- 4.1.1 Linear and Unitary Spaces.- 4.1.2 Linear Operators.- 4.1.3 Special Operators and Eigenvalues.- 4.2 Introduction to the Theory of Representations.- 4.2.1 Operator Representations by Matrices.- 4.2.2 Equivalent Representations and Characters.- 4.2.3 Reducible and Irreducible Representations.- 4.2.4 Orthogonality Theorems.- 4.2.5 Subduction. Reality of Representations.- 4.3 Group Algebra.- 4.3.1 The Regular Representation.- 4.3.2 Projection Operators.- 4.4 Direct Products.- 4.4.1 Representations of Direct Products of Groups.- 4.4.2 The Inner Direct Product of Represel3