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