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# Symmetry

## An Introduction to Group Theory and Its Applications

- 1st Edition - January 1, 1963
- Author: R. McWeeny
- Editor: H. Jones
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 1 2 8 1 - 4
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 2 6 2 4 - 8

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… Read more

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Request a sales quoteSymmetry: 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.

PrefaceChapter 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 GroupChapter 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 ProblemChapter 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 GroupsChapter 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 SpaceChapter 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 ProductChapter 6 Applications Involving Algebraic Forms 6.1 Nature of Applications 6.2 Invariant Forms. Symmetry Restrictions 6.3 Principal Axes. The Eigenvalue Problem 6.4 Symmetry Considerations 6.5 Symmetry Classification of Molecular Vibrations 6.6 Symmetry Coordinates in Vibration TheoryChapter 7 Applications Involving Functions and Operators 7.1 Transformation of Functions 7.2 Functions of Cartesian Coordinates 7.3 Operator Equations. Invariance 7.4 Symmetry and the Eigenvalue Problem 7.5 Approximation Methods. Symmetry Functions 7.6 Symmetry Functions by Projection 7.7 Symmetry Functions and Equivalent Functions 7.8 Determination of Equivalent FunctionsChapter 8 Applications Involving Tensors and Tensor Operators 8.1 Scalar, Vector and Tensor Properties 8.2 Significance of the Metric 8.3 Tensor Properties. Symmetry Restrictions 8.4 Symmetric and Antisymmetric Tensors 8.5 Tensor Fields. Tensor Operators 8.6 Matrix Elements of Tensor Operators 8.7 Determination of Coupling CoefficientsAppendix 1 Representations Carried by Harmonic FunctionsAppendix 2 Alternative Bases for Cubic GroupsIndex

- No. of pages: 262
- Language: English
- Edition: 1
- Published: January 1, 1963
- Imprint: Pergamon
- Paperback ISBN: 9781483212814
- eBook ISBN: 9781483226248

HJ

### H. Jones

Affiliations and expertise

University of Sheffield, Sheffield, UKRM

### R. McWeeny

Affiliations and expertise

Universita di pisaRead

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