Symmetry : An Introduction to Group Theory and its Applications

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This well-organized volume develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion, leading students to a point at which they can proceed easily to more elaborate applications. The finite groups describing the symmetry of regular polyhedra ashow more

Product details

  • Paperback | 256 pages
  • 137.16 x 210.82 x 15.24mm | 226.8g
  • Dover Publications Inc.
  • New York, United States
  • English
  • Unabridged
  • Unabridged
  • 0486421821
  • 9780486421827
  • 81,320

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 Indexshow more