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    Symmetry: An Introduction to Group Theory and its Applications (Dover Books on Physics) (Paperback) By (author) Roy McWeeny

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    DescriptionThe crucial significance of symmetry to the development of group theory and in the fields of physics and chemistry cannot be overstated, and this well-organized volume provides an excellent introduction to the topic. The text develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion, leading students to a point from which they can proceed easily to more elaborate applications. The finite groups describing the symmetry of regular polyhedral and of repeating patterns are emphasized, and geometric illustrations of all main processes appear here -- including more than 100 fully worked examples. Designed to be read at a variety of levels and to allow students to focus on any of the main fields of application, this volume is geared toward advanced undergraduate and graduate physics and chemistry students with the requisite mathematical background.


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    Title
    Symmetry
    Subtitle
    An Introduction to Group Theory and its Applications
    Authors and contributors
    By (author) Roy McWeeny
    Physical properties
    Format: Paperback
    Number of pages: 256
    Width: 136 mm
    Height: 215 mm
    Thickness: 19 mm
    Weight: 272 g
    Language
    English
    ISBN
    ISBN 13: 9780486421827
    ISBN 10: 0486421821
    Classifications

    B&T Book Type: NF
    BIC E4L: SCI
    Nielsen BookScan Product Class 3: S7.9T
    BIC subject category V2: PH
    B&T Merchandise Category: SCI
    B&T General Subject: 710
    Warengruppen-Systematik des deutschen Buchhandels: 26400
    LC subject heading:
    Ingram Subject Code: MA
    Libri: I-MA
    LC subject heading:
    BISAC V2.8: SCI055000
    LC subject heading:
    BISAC V2.8: MAT014000
    DC21: 512.2
    BISAC V2.8: MAT003000, SCI013000
    LC subject heading:
    DC22: 512.2, 512/.2
    LC classification: QD453.3.G75 M38 2002, QD453.3.G7
    Edition
    Unabridged
    Edition statement
    Unabridged
    Publisher
    Dover Publications Inc.
    Imprint name
    Dover Publications Inc.
    Publication date
    28 March 2003
    Publication City/Country
    New York
    Table of contents
     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 groups Index