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| Preface | |
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| Symmetry and physics | |
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| Introduction | |
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| Hamiltonians, eigenfunctions, and eigenvalues | |
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| Symmetry operators and operator algebra | |
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| Point-symmetry operations | |
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| Applications to quantum mechanics | |
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| Exercises | |
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| Symmetry and group theory | |
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| Groups and their realizations | |
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| The symmetric group | |
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| Computational aspects | |
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| Classes | |
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| Homomorphism, isomorphism, and automorphism | |
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| Direct- or outer-product groups | |
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| Exercises | |
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| Group representations: concepts | |
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| Representations and realizations | |
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| Generation of representations on a set of basis functions | |
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| Exercises | |
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| Group representations: formalism and methodology | |
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| Matrix representations | |
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| Character of a matrix representation | |
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| Burnside's method | |
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| Exercises | |
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| Computational projects | |
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| Dixon's method for computing group characters | |
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| The eigenvalue equation modulo p | |
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| Dixon's method for irreducible characters | |
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| Computer codes for Dixon's method | |
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| Finding eigenvalues and eigenvectors | |
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| Exercises | |
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| Appendix 2 | |
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| Computation project | |
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| Group action and symmetry projection operators | |
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| Group action | |
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| Symmetry projection operators | |
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| The regular projection matrices: the simple characteristic | |
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| Exercises | |
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| Construction of the irreducible representations | |
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| Eigenvectors of the regular Rep | |
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| The symmetry structure of the regular Rep eigenvectors | |
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| Symmetry projection on regular Rep eigenvectors | |
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| Computer construction of Irreps with d[subscript alpha] > 1 | |
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| Summary of the method | |
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| Exercise | |
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| Product groups and product representations | |
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| Introduction | |
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| Subgroups and cosets | |
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| Direct outer-product groups | |
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| Semidirect product groups | |
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| Direct inner-product groups and their representations | |
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| Product representations and the Clebsch-Gordan series | |
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| Computer codes | |
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| Summary | |
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| Exercises | |
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| Induced representations | |
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| Introduction | |
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| Subduced Reps and compatibility relations | |
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| Induction of group Reps from the Irreps of its subgroups | |
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| Irreps induced from invariant subgroups | |
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| Examples of Irrep induction using the method of little-groups | |
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| Frobenius reciprocity theorem and other useful theorems | |
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| Exercises | |
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| Crystallographic symmetry and space-groups | |
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| Euclidean space | |
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| Crystallography | |
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| The perfect crystal | |
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| Space-group operations: the Seitz operators | |
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| Symmorphic and nonsymmorphic space-groups | |
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| Site-symmetries and the Wyckoff notation | |
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| Fourier space crystallography | |
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| Exercises | |
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| Space-groups: Irreps | |
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| Irreps of the translation group | |
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| Induction of Irreps of space-groups | |
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| Exercises | |
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| Time-reversal symmetry: color groups and the Onsager relations | |
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| Introduction | |
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| The time-reversal operator in quantum mechanics | |
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| Spin-1/2 and double-groups | |
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| Magnetic and color groups | |
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| The time-reversed representation: theory of corepresentations | |
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| Theory of crystal fields | |
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| Onsager reciprocity theorem (Onsager relations) and transport properties | |
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| Exercises | |
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| Tensors and tensor fields | |
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| Tensors and their space-time symmetries | |
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| Construction of symmetry-adapted tensors | |
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| Description and classification of matter tensors | |
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| Tensor field representations | |
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| Exercises | |
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| Electronic properties of solids | |
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| Introduction | |
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| The one-electron approximations and self-consistent-field theories | |
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| Methods and techniques for band structure calculations | |
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| Electronic structure of magnetically ordered systems | |
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| Derivation of the Hartree-Fock equations | |
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| Holstein-Primakoff (HP) operators | |
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| Exercises | |
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| Dynamical properties of molecules, solids, and surfaces | |
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| Introduction | |
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| Dynamical properties of molecules | |
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| Dynamical properties of solids | |
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| Dynamical properties of surfaces | |
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| Coulomb interactions and the method of Ewald summations | |
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| Electronic effects on phonons in insulators and semiconductors | |
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| Exercises | |
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| Experimental measurements and selection rules | |
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| Introduction | |
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| Selection rules | |
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| Differential scattering cross-sections in the Born approximation | |
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| Light scattering spectroscopies | |
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| Photoemission and dipole selection rules | |
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| Neutron and atom scattering spectroscopies | |
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| Exercises | |
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| Landau's theory of phase transitions | |
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| Phase transitions and their classification | |
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| Landau theory of phase transitions: principles | |
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| Construction and minimization techniques for [Delta phi] | |
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| Exercises | |
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| Incommensurate systems and quasi-crystals | |
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| Introduction | |
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| The concept of higher-dimensional spaces: superspaces and superlattices | |
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| Quasi-crystal symmetry: the notion of indistinguishability and the classification of space-groups | |
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| Two-dimensional lattices, cyclotomic integers, and axial stacking | |
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| Bibliography | |
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| References | |
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| Index | |