The mathematical theory of symmetry in solids : representation theory for point groups and space groups / by Christopher Bradley, Arthur Cracknell.

Format:

Book

Author/Creator:

Bradley, C. J. (Christopher John), author.

Cracknell, Arthur P., author.

Series:

Oxford classic texts in the physical sciences.

Oxford scholarship online.

Oxford classic texts in the physical sciences

Oxford scholarship online

Language:

English

Subjects (All):

Solid state physics.

Representations of groups.

Symmetry (Physics).

Physical Description:

1 online resource (758 p.)

Edition:

1st ed.

Place of Publication:

Oxford : Oxford University Press, 2023.

Language Note:

English

Summary:

This book gives, in extensive tables, the irreducible representations of the crystallographic point groups and space groups. These are useful in studying the eigenvalues and eigenfunctions of a particle or quasi-particle in a crystalline solid. The theory is extended to the corepresentations of the Shubnikov groups.

Contents:

""CONTENTS""; ""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""; ""5. THE SINGLE-VALUED REPRESENTATIONS OF THE 230 SPACE GROUPS""; ""5.1. Abstract groups""; ""5.2. The single-valued representations of the 230 space groups""

""5.3. The labels of space-group representations""""5.4. Example of the use of the tables of the space-group representations""; ""5.5. Representation domain and basic domain""; ""6. THE DOUBLE-VALUED REPRESENTATIONS OF THE 32 POINT GROUPS AND THE 230 SPACE GROUPS""; ""6.1. The double-valued representations of the point groups""; ""6.2. Symmetry-adapted functions for double point groups""; ""6.3. The double-valued representations of the space groups""; ""6.4. An example of the deduction of the representations of a double space group""

""6.5. The double-valued representations of the 230 space groups""""7. THE MAGNETIC GROUPS AND THEIR COREPRESENTATIONS""; ""7.1. The Shubnikov groups and their derivation""; ""7.2. The classification of Shubnikov groups""; ""7.3. Anti-unitary operations and the corepresentations of magnetic groups""; ""7.4. The Kronecker products of corepresentations""; ""7.5. The corepresentations of the magnetic point groups""; ""7.6. The corepresentations of the magnetic space groups""; ""7.7. Example: the space-group corepresentations of P4'[sub(2)]/mnm' and their Kronecker products""

""7.8. Spin-space groups""

Notes:

Formerly CIP.

Previously issued in print: 2009.

Includes bibliographical references and index.

Derived record based on print version record and publisher information.

ISBN:

0-19-170233-1

0-19-157689-1

OCLC:

922972478