The mathematical theory of symmetry in solids : representation theory for point groups and space groups / by C.J. Bradley and A.P. Cracknell.

Includes bibliographies and index.

1 Symmetry and The Solid State ; 1.1 Introduction ; 1.2 Group theory ; 1.3 Group representations ; 1.4 Point groups ; 1.5 Space groups -- 2 Symmetry-Adapted Functions for the Point Groups ; 2.1 The matrix elements of the rotation group ; 2.2 The generation of symmetry-adapted functions ; 2.3 Application to the point groups ; 2.4 Symmetry-adapted functions for the crystallographic point groups ; 2.5 Active and passive operators ; 2.6 Symmetrized and anti-symmetrized products of point-group representations -- 3 Space Groups ; 3.1 Bravais lattices ; 3.2 Reciprocal lattices and Brillouin zones ; 3.3 The classification of points and lines of symmetry ; 3.4 The irreducible representations of the translation groups ; 3.5 The classification of the 230 3-dimensional space groups ; 3.6 The action of space-group operations on Bloch functions ; 3.7 A descriptive account of the representation theory of space groups ; 3.8 Examples: cubic close-packed and diamond structures -- 4 The Representations of A Group in Terms of The Representations of An Invariant Subgroup ; 4.1 Induced representations ; 4.2 Groups with an invariant subgroup ; 4.3 The theory of little groups ; 4.4 The small representations of little groups ; 4.5 The point groups as semi-direct products ; 4.6 The reality of representations induced from little groups ; 4.7 Direct products of induced representations ; 4.8 Symmetrized and anti-symmetrized squares of induced representations

"This book gives the complete theory of the irreducible representations of the crystallographic point groups and space groups. This is important in the quantum-mechanical study of a particle or quasi-particle in a molecule or crystalline solid because the eigenvalues and eigenfunctions of a system belong to the irreducible representations of the group of symmetry operations of that system. The theory is applied to give complete tables of these representations for all the 32 point groups and 230 space groups, including the double-valued representations. For the space groups, the group of the symmetry operations of the k vector and its irreducible representations are given for all the special points of symmetry, lines of symmetry and planes of symmetry in the Brillouin zone. Applications occur in the electronic band structure, phonon dispersion relations and selection rules for particle-quasiparticle interactions in solids. The theory is extended to the corepresentations of the Shubnikov (black and white) point groups and space groups."--pub. desc.

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