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| Laurens Jansen — Theory of Finite Groups. Applications in Physics |
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| Предметный указатель |
Abelian group(s) 4
Abelian group(s), direct sum of 42 54 57 58
Abelian group(s), sum of 42 54 57 58
Abstract (or External) direct product 43
Abstract (or External) direct product, infinite 57
Abstract (or External) direct product, multiple finite 52
Abstract crystallographic point-group 354
Abstract point-group 352
Accidental degeneracy 211
Adjoint of operator see "Hermitian conjugate of operator"
Admissible homomorphism (or  -homomorphism) 62
Admissible subgroup see "Stable subgroup"
Admissible subset of operator group 62
Affine group (3-dimensional real) 241
Algebraic structure of set 1
Allowable representation 149
Alternating representation 236
Ambivalent conjugation class 31
Antilinear operator 170 193
Antisymmetrization operator 234
Antiunitary operator 195
Associate representation 149
Associate set of representations 149
Associative law for a group 2
Associative property for operators 195
Automorphism (or Automorphic mapping) 20
Automorphism (or Automorphic mapping), inner see "Conjugation"
Basic Brillouin zone see "First Brillouin zone"
Black-white point-groups see "Shubnikov point-groups"
Bloch-condition 249
Bravais lattice 353
Brillouin zone, first 249
Brillouin zone, proper 258
Canonical homomorphism see "Natural homomorphism"
Carrier space 79
Center of a group 15
Center of a ring 68
centralizer 15
Character (or Character vector) of representation 97
Character table 105
Charge conjugation (operator) 294 310 314
Class constants (or Class multiplication coefficients) 32
Class function 112
Class of group see "Conjugation class"
Class of set see "Equivalence class"
Class-constant equations 32
Clifford's theorem 146
Closure, under multiplication 2
Co-representation(s) 171
Co-representation(s), basic theorem for 174
Co-representation(s), irreducible 173 179—180
Co-representation(s), reducible 173
Commutation of operators 195
Commutation of subgroups 39
Commutative group see "Abelian group"
Commutative law 3
Commutator in a group 74
Commutator subgroup 74
Commuting ring of representation 100
Complement of subspace 196
Complement of subspace, orthogonal 196
Complete orthonormal set of vectors 191
Complete vector space 190
Completely decomposed representation 95
Completely reduced representation 94
Completeness of Hilbert space 190
Complex conjugate representations 125ff.
Complex conjugate representations, character test for 130
Complex conjugation operator 170 216 281
Composite group 34
Composition law for elements of set 1
Composition law for elements of set, inner and outer 5
Composition law for group elements 2
Congruency 35 36
Congruent elements 35
Conjugate elements 25
Conjugate representations 142
Conjugate subgroups 33
Conjugation 23—24
Conjugation class 26
Conjugation class, ambivalent 31
Conjugation class, order of 30
Coset 15
Coset decomposition of group 17
Coset representative 17
Coset, left and right 16
Crystallographic point-groups 161 188 217 238 241 334 352ff.
Crystallographic point-groups, abstract 354
Crystallographic space-groups see "Space-groups"
Cubic group 347
Cycle structure of permutation 27—28
Cyclic boundary conditions 245
Cyclic groups 8 119 345 346
Decomposable group 55
Decomposable representation 94
Decomposition of vector space or linear manifold 196
Decomposition of vector space or linear manifold, orthogonal 196
Degeneracy of eigenfunctions 200 210—213 281ff.
Degeneracy of eigenfunctions, accidental 211
Dense subgroup 57
Dense subset 193—194
Dihedral groups 346
Dirac equation of motion 292
Dirac equation of motion with external electromagnetic field 294
Dirac Hamiltonian 293
Dirac matrices 292 301
Dirac matrices, Fundamental Theorem of 301
Dirac matrix group 299
Dirac operator 292
Dirac operator with external electromagnetic field 294
Direct factor of group 41
Direct product of groups 41
Direct product of groups, infinite 57
Direct product of groups, irreducible representations of 153ff.
Direct product of groups, multiple finite 51
Direct sum of abelian groups 42
Direct sum of abelian groups, infinite 57 58
Direct sum of abelian groups, multiple finite 54
Direct sum of subspaces or linear manifolds 196
Direct summand of abelian group 54
Disjoint cycles in permutations 27—28
Disjoint sets 13
Disjoint vector spaces or linear manifolds 92 196
Distributivity of composition laws 66—67
Division ring see "Field"
Double group 205 261ff.
Double point-group 269
Double space-group 243 261ff.
Double translation group 268
Double-valued representation see "Spin representation"
Eigenfunction(s) 188 200
Eigenfunction(s), degenerate 200 210—213 281ff.
Eigenspace 201
Endomorphism (or Endomorphic mapping) 20n 59
Energy band 257
Engendered representation 152
Epimorphism (or Epimorphic mapping) 20n
Equilateral triangle, group of 9
Equivalence class 24
Equivalence relation 24
Equivalent plane waves 250
Equivalent representations 83
Equivalent vectors in reciprocal space 247
Euclidean group (in 3 dimensions) 307
Euclidean metric 86
Euclidean space 61 85—86
Euler's theorem 335 338—339
Exclusion principle (Pauli) 234—236
Extra representation 273—274
Factor group 36
| Faithful representation 76
Fiber in mapping 18
Field 5 70
Field, skew 70
First Brillouin zone 249
Four-group 39 157
Four-potential 293
Frobenius' reciprocity theorem 139—140
Frobenius' theorem on subduced representations 137
Fundamental domain of k see "First Brillouin zone"
Gauge transformation 218n 219 294—295
General k-vector 252
Generating element (or Generator) of cyclic group 8 119
Grey point-groups 355
Group algebra 78 224—225
Group homomorphism 19ff.
Group projection operator 225ff.
Group with operators see "Operator group"
Group(s) of equilateral triangle 9
Group(s) of square 113—115
Group(s) of the electromagnetic potential 321
Group(s), Abelian 4
Group(s), abstract (or external) direct product of 43 52 57
Group(s), abstract point- 348
Group(s), affine see "Real affine"
Group(s), black-white point- see "Shubnikov point-group(s)"
Group(s), center of 15
Group(s), commutative see "Group(s) abelian"
Group(s), composite 34
Group(s), crystallographic point- 161 188 217 238 241 334 352ff.
Group(s), cubic 347
Group(s), cyclic 8 119 345 346
Group(s), decomposable 55
Group(s), definition of 2
Group(s), dihedral 346
Group(s), dimensions 241
Group(s), Dirac matrix 299
Group(s), direct product of 41 51 57 153ff.
Group(s), direct sum of abelian 42 54 57 58
Group(s), double 205 261ff.
Group(s), double point- 269
Group(s), double space- 243 261ff.
Group(s), double translation 268
Group(s), Euclidean (in 3 dimensions) 307
Group(s), factor 36
Group(s), four- 39 157
Group(s), grey point- 355
Group(s), icosahedral 348
Group(s), indecomposable 55
Group(s), invariance (of Hamiltonian) 214
Group(s), inversion (in space-time) 306
Group(s), little 143—144
Group(s), Lorentz 306—307
Group(s), magnetic double point- 323
Group(s), magnetic point- 354 356
Group(s), matrix 83
Group(s), octahedral see "Group(s) cubic"
Group(s), of the k-vector 252
Group(s), order of 5
Group(s), orthochronous Lorentz 306—307
Group(s), orthochronous Poincare 306
Group(s), permutation 6 9—10 115ff. 236
Group(s), Poincare 304ff.
Group(s), point- 9 334ff. see
Group(s), postulates for 2—5
Group(s), primary 55—56
Group(s), product of 39 51 57
Group(s), proper Lorentz 307n
Group(s), proper orthochronous Lorentz 307
Group(s), proper orthochronous Poincare 306
Group(s), proper Poincare 307n
Group(s), proper point- 341 348—349
Group(s), quotient see "Group(s) factor"
Group(s), real affine in 3
Group(s), real orthogonal see "Group(s) rotation-inversion"
Group(s), restricted Lorentz see "Group(s) proper
Group(s), rotation (in 3 dimensions) 27 335
Group(s), rotation-inversion (in 3 dimensions) 307 334
Group(s), semidirect product of 41 46ff. 60 157ff.
Group(s), Shubnikov point- 354—355
Group(s), simple 34
Group(s), single 205
Group(s), space- 188 217 233 236ff.
Group(s), square lattice- 259—261
Group(s), substitutional 213 215ff. 242—243
Group(s), sum of abelian 42 54 57 58
Group(s), symmetric see "Group(s) permutation"
Group(s), symmetry 203ff. 213ff.
Group(s), symmetry-operator ray 204—207
Group(s), symmorphic space- 161 241 242
Group(s), tetrahedral 48 347
Group(s), translation 239 246ff.
Group(s), weak direct product of 49
Hamilton operator (or Hamiltonian) 189 201ff.
Hamilton operator (or Hamiltonian) for systems without spin 213 237
Hamilton operator (or Hamiltonian), Dirac 293
Hamilton operator (or Hamiltonian), Pauli — Schroedinger 328
Hamilton operator (or Hamiltonian), Pauli — Schroedinger with spin-orbit coupling 262 329
Hermitian conjugate operator 86—87 194
Hermitian operator 194—195
Hermitian scalar product see "Scalar product"
Hilbert space 189ff.
Hilbert space, separable 191
Holomorph of a group 47
Homomorphism (or Homomorphic mapping) 19
Homomorphism (or Homomorphic mapping), admissible (or operator or -) 62
Homomorphism (or Homomorphic mapping), canonical (or natural) 37
Homomorphism (or Homomorphic mapping), group 19ff.
Homomorphism (or Homomorphic mapping), multiplicity of 22
Homomorphism (or Homomorphic mapping), ring 67
Homomorphism condition 18—19 88 215
Homomorphism condition for space-groups 243—244
Icosahedral group 348
Ideal 68
Ideal, left and right 68
Ideal, two-sided 68
Idempotent operator 197
Identity element 3—5
Identity element, left and right 3
Identity operator 193
Identity representation 77 112
Image under group homomorphism 19
Image under mapping 18
Improper point-operation (in 3-dimensional Euclidean space) 238 335
Improper subgroup 13
Indecomposable group 55
Indecomposable representation 94
Index of subgroup 16
Induced representation 133—135 138ff.
Inhomogeneous Lorentz transformation see "Poincare transformation"
Inner automorphism see "Conjugation"
Inner product see "Scalar product"
Intersection of sets 12
Invariance group of Hamiltonian 214
Invariance transformation 214
Invariant subgroup see "Normal subgroup"
Inverse element of group 3—5
Inverse element of group, left and right 3
Inverse operator 194
Inversion group (in space-time) 306
Inversion operator, space- (in 3-dimensional Euclidean space) 238 334
Inversion operator, space- (in space-time) 306
Inversion operator, space-time- 306
Inversion operator, time- 305
Irreducibility criterion for representation 107
Irreducibility Postulate 204 11
Irreducible co-represcntation 173 179—180
Irreducible representation 79 80 92ff.
Isomorphism (or Isomorphic mapping) 19ff.
Isomorphism (or Isomorphic mapping), group 8 19ff.
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