Symmetry An Introduction to Group Theory and Its Applications,9780486421827

Symmetry An Introduction to Group Theory and Its Applications

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Edition: Unabridged
ISBN13: 9780486421827
ISBN10: 0486421821
Format: Paperback
Pub. Date: 2002-06-12
Publisher(s): Dover Publications
List Price: $17.01

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Summary

This well-organized volume develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion. Designed to allow students to focus on any of the main fields of application, it is geared toward advanced undergraduate and graduate physics and chemistry students. 1963 edition. Appendices.

Table of Contents

Preface vii
Groups
Symbols and the group property
1(5)
Definition of a group
6(1)
The multiplication table
7(2)
Powers, products, generators
9(2)
Subgroups, cosets, classes
11(2)
Invariant subgroups. The factor group
13(1)
Homomorphisms and isomorphisms
14(2)
Elementary concept of a representation
16(2)
The direct product
18(1)
The algebra of a group
19(3)
Lattices and Vector Spaces
Lattices. One dimension
22(3)
Lattices. Two and three dimensions
25(2)
Vector spaces
27(1)
n-Dimensional space. Basis vectors
28(3)
Components and basis changes
31(2)
Mappings and similarity transformations
33(5)
Representations. Equivalence
38(3)
Length and angle. The metric
41(6)
Unitary transformations
47(2)
Matrix elements as scalar products
49(2)
The eigenvalue problem
51(3)
Point and Space Groups
Symmetry operations as orthogonal transformations
54(5)
The axial point groups
59(10)
The tetrahedral and octahedral point groups
69(6)
Compatibility of symmetry operations
75(3)
Symmetry of crystal lattices
78(7)
Derivation of space groups
85(6)
Representations of Point and Translation Groups
Matrices for point group operations
91(4)
Nomenclature. Representations
95(10)
Translation groups. Representations and reciprocal space
105(4)
Irreducible Representations
Reducibility. Nature of the problem
109(1)
Reduction and complete reduction. Basic theorems
110(6)
The orthogonality relations
116(5)
Group characters
121(3)
The regular representation
124(1)
The number of distinct irreducible representations
125(1)
Reduction of representations
126(5)
Idempotents and projection operators
131(2)
The direct product
133(7)
Applications Involving Algebraic Forms
Nature of applications
140(1)
Invariant forms. Symmetry restrictions
141(6)
Principal axes. The eigenvalue problem
147(3)
Symmetry considerations
150(1)
Symmetry classification of molecular vibrations
151(8)
Symmetry coordinates in vibration theory
159(7)
Applications Involving Functions and Operators
Transformation of functions
166(4)
Functions of Cartesian coordinates
170(4)
Operator equations. Invariance
174(7)
Symmetry and the eigenvalue problem
181(6)
Approximation methods. Symmetry functions
187(3)
Symmetry functions by projection
190(5)
Symmetry functions and equivalent functions
195(2)
Determination of equivalent functions
197(6)
Applications Involving Tensors and Tensor Operators
Scalar, vector and tensor properties
203(3)
Significance of the metric
206(2)
Tensor properties. Symmetry restrictions
208(3)
Symmetric and antisymmetric tensors
211(7)
Tensor fields. Tensor operators
218(6)
Matrix elements of tensor operators
224(7)
Determination of coupling coefficients
231(4)
Appendix 1 Representations carried by harmonic functions 235(6)
Appendix 2 Alternative bases for cubic groups 241(4)
Index 245

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