preface 1 symmetry and physics 1.1 introduction 1.2 hamiltonians, eigenfunctions, and eigenvalues 1.3 symmetry operators and operator algebra 1.4 point-symmetry operations 1.5 applications to quantum mechanics exercises 2 symmetry and group theory 2.1 groups and their realizations 2.2 the symmetric group 2.3 computational aspects 2.4 classes 2.5 homomorphism, isomorphism, and automorphism 2.6 direct- or outer-product groups exercises 3 group representations: concepts 3.1 representations and realizations 3.2 generation of representations on a set of basis functions exercises 4 group representations: formalism and methodology 4.1 matrix representations 4.2 character of a matrix representation 4.3 burnside's method exercises computational projects 5 dixon's method for computing group characters 5.1 the eigenvalue equation modulo p 5.2 dixon's method for irreducible characters 5.3 computer codes for dixon's method appendix 1 finding eigenvalues and eigenvectors exercises appendix 2 computation project 6 group action and symmetry projection operators 6.1 group action 6.2 symmetry projection operators 6.3 the regular projection matrices: the simplecharacteristic exercises 7 construction of the irreducible representations 7.1 eigenvectors of the regular rep 7.2 the symmetry structure of the regular rep eigenvectors 7.3 symmetry projection on regular rep eigenvectors 7.4 computer construction of irreps with ds ]1 7.5 summary of the method exercise 8 product groups and product representations 8.1 introduction 8.2 subgroups and cosets 8.3 direct outer-product groups 8.4 semidirect product groups 8.5 direct inner-product groups and their representations 8.6 product representations and the clebsch-gordan series 8.7 computer codes 8.8 summary exercises 9 induced representations 9.1 introduction 9.2 subduced reps and compatibility relations 9.3 induction of group reps from the irreps of its subgroups 9.4 irreps induced from invariant subgroups 9.5 examples of irrep induction using the method oflittle-groups appendix frobenius reciprocity theorem and other usefultheorems exercises 10 crystallographic symmetry and space-groups 10.1 euclidean space 10.2 crystallography 10.3 the perfect crystal 10.4 space-group operations: the seitz operators 10.5 symmorphic and nonsymmorphic space-groups 10.6 site-symmetries and the .wyckoff notation 10.7 fourier space crystallography exercises 11 space-groups: irreps 11.1 irreps of the translation group 11.2 induction of irreps of space-groups exercises 12 time-reversal symmetry: color groups and the onsagerrelations 12.1 introduction 12.2 the time-reversal operator in quantum mechanics 12.3 spin-l/2 and double-groups 12.4 magnetic and color groups 12.5 the time-reversed representation: theory ofcorepresentations 12.6 theory of crystal fields 12.7 onsager reciprocity theorem (onsager relations) and transportproperties exercises 13 tensors and tensor fields 13.1 tensors and their space-time symmetries 13.2 construction of symmetry-adapted tensors 13.3 description and classification of matter tensors 13.4 tensor field representations exercises 14 electronic properties of solids 14.1 introduction 14.2 the one-electron approximations and self-consistent-fieldtheories 14.3 methods and techniques for band structure calculations 14.4 electronic structure of magnetically ordered systems appendix i derivation of the hartree-fock equations appendix 2 holstein-primakoff (hp) operators exercises 15 dynamical properties of molecules, solids, and surfaces 15.1 introduction 15.2 dynamical properties of molecules 15.3 dynamical properties of solids 15.4 dynamical properties of surfaces appendix 1 coulomb interactions and the method of ewaldsummation appendix 2 electronic effects on phonons in insulators andsemiconductors exercises 16 experimental measurements and selection rules 16.1 introduction 16.2 selection rules 16.3 differential scattering cross-sections in the bornapproximation 16.4 light scattering spectroscopies 16.5 photoemission and dipole selection rules 16.6 neutron and atom scattering spectroscopies exercises 17.1 phase transitions and their classification 17.2 landau theory of phase transitions: principles 17.3 construction and minimization techniques for △φ exercises 18 incommensurate systems and quasi-crystals 18.1 introduction 18.2 the concept of higher-dimensional spaces: superspaces andsuperlattices 18.3 quasi-crystal symmetry: the notion of indistinguishability andthe clossification of space-groups 18.4 two-dimensional lattices, cyclotomic integers, and axialstacking bibliography references index
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