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.
Preface Chapter 1 Groups 1.1 Symbols and the Group Property 1.2 Definition of a Group 1.3 The Multiplication Table 1.4 Powers, Products, Generators 1.5 Subgroups, Cosets, Classes 1.6 Invariant Subgroups. The Factor Group 1.7 Homomorphisms and Isomorphisms 1.8 Elementary Concept of a Representation 1.9 The Direct Product 1.10 The Algebra of a Group Chapter 2 Lattices and Vector Spaces 2.1 Lattices. One Dimension 2.2 Lattices. Two and Three Dimensions 2.3 Vector Spaces 2.4 n-Dimensional Space. Basis Vectors 2.5 Components and Basis Changes 2.6 Mappings and Similarity Transformations 2.7 Representations. Equivalence 2.8 Length and Angle. The Metric 2.9 Unitary Transformations 2.10 Matrix Elements as Scalar Products 2.11 The Eigenvalue Problem Chapter 3 Point and Space Groups 3.1 Symmetry Operations as Orthogonal Transformations 3.2 The Axial Point Groups 3.3 The Tetrahedral and Octahedral Point Groups 3.4 Compatibility of Symmetry Operations 3.5 Symmetry of Crystal Lattices 3.6 Derivation of Space Groups Chapter 4 Representations of Point and Translation Groups 4.1 Matrices for Point Group Operations 4.2 Nomenclature. Representations 4.3 Translation Groups. Representations and Reciprocal Space Chapter 5 Irreducible Representations 5.1 Reducibility. Nature of the Problem 5.2 Reduction and Complete Reduction. Basic Theorems 5.3 The Orthogonality Relations 5.4 Group Characters 5.5 The Regular Representation 5.6 The Number of Distinct Irreducible Representations 5.7 Reduction of Representations 5.8 Idempotents and Projection Operators 5.9 The Direct Product Chapter 6 Applications Involving Algebraic Forms 6.1 Nature of Applications 6.2 Invariant Forms. Symmetry Restrictions 6.3 Principal Axes. The Eigenvalue Problem
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- © Pergamon 1963
- 1st January 1963
- eBook ISBN:
Universita di pisa
University of Sheffield, Sheffield, UK