Symmetry An Introduction to Group Theory and Its Applications

ISBN-10: 0486421821
ISBN-13: 9780486421827
Edition: 2002
Authors: Roy McWeeny
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Description: Designed to be read at a variety of levels and to allow readers to focus on any of the main fields of application, this volume develops the elementary ideas of both group theory and representation theory.

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Book details

List price: $15.95
Copyright year: 2002
Publisher: Dover Publications, Incorporated
Publication date: 6/12/2002
Binding: Paperback
Pages: 256
Size: 5.50" wide x 8.75" long x 0.75" tall
Weight: 0.836
Language: English

Designed to be read at a variety of levels and to allow readers to focus on any of the main fields of application, this volume develops the elementary ideas of both group theory and representation theory.

Preface
Groups
Symbols and the group property
Definition of a group
The multiplication table
Powers, products, generators
Subgroups, cosets, classes
Invariant subgroups. The factor group
Homomorphisms and isomorphisms
Elementary concept of a representation
The direct product
The algebra of a group
Lattices and Vector Spaces
Lattices. One dimension
Lattices. Two and three dimensions
Vector spaces
n-Dimensional space. Basis vectors
Components and basis changes
Mappings and similarity transformations
Representations. Equivalence
Length and angle. The metric
Unitary transformations
Matrix elements as scalar products
The eigenvalue problem
Point and Space Groups
Symmetry operations as orthogonal transformations
The axial point groups
The tetrahedral and octahedral point groups
Compatibility of symmetry operations
Symmetry of crystal lattices
Derivation of space groups
Representations of Point and Translation Groups
Matrices for point group operations
Nomenclature. Representations
Translation groups. Representations and reciprocal space
Irreducible Representations
Reducibility. Nature of the problem
Reduction and complete reduction. Basic theorems
The orthogonality relations
Group characters
The regular representation
The number of distinct irreducible representations
Reduction of representations
Idempotents and projection operators
The direct product
Applications Involving Algebraic Forms
Nature of applications
Invariant forms. Symmetry restrictions
Principal axes. The eigenvalue problem
Symmetry considerations
Symmetry classification of molecular vibrations
Symmetry coordinates in vibration theory
Applications Involving Functions and Operators
Transformation of functions
Functions of Cartesian coordinates
Operator equations. Invariance
Symmetry and the eigenvalue problem
Approximation methods. Symmetry functions
Symmetry functions by projection
Symmetry functions and equivalent functions
Determination of equivalent functions
Applications Involving Tensors and Tensor Operators
Scalar, vector and tensor properties
Significance of the metric
Tensor properties. Symmetry restrictions
Symmetric and antisymmetric tensors
Tensor fields. Tensor operators
Matrix elements of tensor operators
Determination of coupling coefficients
Representations carried by harmonic functions
Alternative bases for cubic groups
Index

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