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Laurens Jansen — Theory of Finite Groups. Applications in Physics
Laurens Jansen — Theory of Finite Groups. Applications in Physics

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Название: Theory of Finite Groups. Applications in Physics

Автор: Laurens Jansen

Аннотация:

No part of this book may be reproduced in any form by print or any other means without written permission from the publisher.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st

Год издания: 1967

Количество страниц: 376

Добавлена в каталог: 05.05.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\Omega$-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 $\Omega$-)      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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