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| Tung W.K. — Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions |
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Название: Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions
Автор: Tung W.K.
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1985
Количество страниц: 344
Добавлена в каталог: 17.03.2008
Операции: Положить на полку |
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Abelian group 13
Action transformation 3 263
Addition of linear transformations 298
Addition of vectors 295
Addition theorem 145 164
Adjoint operator for anti-linear operator on the dual vector space 302
Adjoint operator for anti-linear operator on vector space 304
Algebra of linear transformations 298
Alternating group 65
Angular momentum basis 160 170 220 226 238
Angular momentum basis orbital 138
Angular momentum basis spin 138
Annihilation operators 147 206
Anti-linear transformation 248 331
Anti-particle 205
Anti-symmetrizer 65
Anti-unitary operator 249 332
Anti-unitary operator, time-reversal as an 250
Associativity 12 295
Axial vector 231 287
Basis 296
Basis, canonical 105
Basis, vectors 292
Bessel function 158 163
Bessel function, spherical 171
Bispinors 327
Bispinors, symmetric 231
Bloch wave function 7
Boost Lorentz 176 228
Bose — Einstein system 134
Branching ratios 62 123
Casimir operator 103 157 191 195 224
Cayley's theorem 17
Center 24
CHARACTER 32
Character, for direct product representation 49
Character, for rotation group SO(3) 109
Character, table 43
Charge conjugation symmetry 205 212
Charge conservation 10
class 19
Class of permutations 20
Class of the rotation group SO( 3 97
Classical groups 16 80 262
Clebsch — Gordan coefficients 50 120
Commutation relations Lie algebra 101
Commutativity 295
Commutator 101
Compactness of rotation group SO(3) 96
Compactness of SU(2) 127
Compactness of unitary groups 279
Complementary series 191 330
Completeness of irreducible representation matrices 8 41 47
Completeness of spherical harmonics 146
Condon — Shortley phase convention 105 120
Conjugate group elements 19
Conjugate subgroup 20
Conjugate vector space 265
Continuous groups 15 80 290
Contraction 265 266 270 323 325
Contractions by invariant tensor 282
Contractions by the metric tensor 284
Contravariant four-vector 177
Contravariant vector components 292 323
Contravariant vector with dotted index 265
Coordinate transformation 263
Coset 21 215
Covariant four-vector 178
Covariant normalization 201
Covariant vector components 264 292
Covariant vector with dotted index 265
Covering group 125 181
Creation operators 147 206
Cycle notation 17
Cycle structure 17
Cyclic group 13
Degenerate representation 27
Dihedral group 14 213
Dimension of group representations 27
Dirac equation 203 210
Dirac spinor 230 326
Direct product of operators 49
Direct product of representations 49 117
Direct product of vector spaces 265 270 276
Direct sum 297
Discrete rotational symmetry 10
Distributive law 296
Dotted contravariant index 265 325
Dotted covariant index 265 324
Dual basis 301
Dual diagram 281
Dual vector space 264 301
Dummy index 292
Einstein convention 292
Electric multipole 242
Electromagnetic 4-potential 147 189
electromagnetic field 117 147 189 327
Energy band 8
Energy gap 8
Equivalence of group representations 32
Equivalence of tensor representations 274
Equivalence relation 19 296
Euclidean group 152
Euclidian group in three dimensions 166 223
Euclidian group in two dimensions 154 218
Euler angles 97
Event 174
Extended Euclidean group in two dimensions 218
Extended Euclidian group in three dimensions 223
Extended Poincar group 231
Fermi — Dirac system 134
Field operator, relativistic 203
Final state interaction 261
Four-group 13
Four-momentum operator 183
Four-vector 177
Four-vector, length of a four-vector 174
Four-vector, light-like 179
Four-vector, space-like 178
Four-vector, time-like 178
Fourier generalization of 134
Fourier series 8
Fourier theorem 8 91
Full Poincare group 246
Fundamental representations of the general linear group GL(m) 264
Fundamental representations of the Lorentz group SL(2,C) 189 320
Future cone 178
Gauge Coulomb 147
Gauge invariance 10
General linear group 15 70 263
General linear group, real 277
Generators 84
Generators of Euclidean groups 154 166
Generators of Lie groups 289
Generators of rotation groups 84 99
Generators of the Lorentz group 183
Generators of translations 90 154 182
Group 5 12
Group Abelian 13
Group algebra 45 307
Group continuous 15
Group contraction 166
Group cyclic 13
Group definition 12
Group dihedral 14
Group factor 22
Group general linear 15
Group multiplication 12
Group multiplication table 12
Group multiplication, table of 13
| Group non-Abelian 14
Group of linear transformations 27
Group of motion 152
Group of translations discrete 5
Group of translations in one dimension 90
Group orthogonal 16 214 283
Group permutation 16 64
Group point 10
Group quotient 22
Group semi-simple 21 290
Group simple 21
Group space 10
Group special linear 180 280 320
Group special unitary 16 125 283
Group symmetric 16 64
Group unitary 16 277
Hamiltonian 2 122 149 183 246 259
Hamiltonian interacting 149 259
Helicity 136 168 199 226 257
Helicity states 139 194 199 234
Hermitian conjugate 305
Hermitian metric tensor 278
Hermitian operators 305
Homogeneity of space 9
Homogeneity of space-time 174
Homogeneity of time 9
Homogeneous Lorentz group 174
Homomorphism 23
Ideal left 309
Ideal two-sided 313
Idempotent 299 310
Idempotent condition for inequivalence 311
Idempotent condition to be primitive 310
Idempotent essentially 310
Identical particles 64
Identity element of a group 12
Identity representation 28
Identity transformation 15
Induced representation 160 166 196
Infinitesimal transformations Generators 83 183
Inner product 302
Inner product space 302
Internal symmetry 11
Intrinsic parity 218 226 232
Intrinsic spin 136
Invariant group integration measure of SO(2) 87
Invariant group integration measure of SO(3) and SU(2) 129
Invariant subgroup 20
Invariant subgroup Abelian 21
Invariant subgroup of Euclidean groups 160 168
Invariant subgroup of the PoincarS 182
Invariant subspace 33
Invariant subspace irreducible 35 56
Invariant subspace minimal 33
Invariant subspace proper 33 35
Invariant tensors 95 175 262 267 270 278 280
Inverse 12
Irreducibility, necessary and sufficient condition of 45
Irreducible representations of Abelian groups 37
Irreducible representations of Euclidean groups 158 169 220 225
Irreducible representations of general linear groups 77 274 276
Irreducible representations of orthogonal groups 217 223 285
Irreducible representations of rotation groups 85 105
Irreducible representations of special linear groups 189 281
Irreducible representations of symmetric groups 70
Irreducible representations of the Lorentz group 187 191 230
Irreducible representations of the Poincare group 193 196 198 199 233 235
Irreducible representations of unitary groups 280
Irreducible set of basis vectors 54
Irreducible set of fields 114
Irreducible set of operators 60 115
Irreducible set of wave function 114
Irreducible tensors 60 115
Irreducible tensors of SO(3) and SU(2) 128
Isomorphism 17 296
Isotopic spin invariance 11
Isotropy of space 10
Isotropy of space-time 174
Kernel 24
Klein — Gordon equation 204
Lattice one-dimensional 2
Lattice rotational symmetry on 10
Lattice translational symmetry on 10
Left coset 21
Left ideal 309
Left ideal minimal 309
Length of four-vectors 174
Length of vectors 302
Lie algebra of Euclidean groups 155 167
Lie algebra of the PoincarS group 185
Lie algebra of the proper Lorentz group 186
Lie algebra of the rotation group 101—102
Lie group 80 290
Light-cone 178
linear combination 296
Linear dependence 296
Linear functional 265 301
Linear independence 296
Linear momentum basis plane wave states
Linear momentum operator 93
Linear transformation 297
Linear transformation, symmetry-preserving 78 316
Linear vector space 295
Little group 160 168 180 193 196 199
Lorentz boost 176 184
Lorentz group, complete 227
Lorentz group, finite dimensional representations of 188
Lorentz group, inhomogeneous 181
Lorentz group, proper 177
Lorentz group, unitary representations of 189 328
Lorentz invariant 323
Lorentz scalar 323
Lorentz transformation 10 174
Lorentz transformation as “rotation” in x-t plane 177
Lorentz transformation special 176
Lorentz vector 177
Lowering operator 103 157
Magnetic multipole 242
Mass 192
Matrix group 15
Maxwell equations 202
Metric Minkowski 174
Metric tensor 174 278
Minkowski metric 174
Minkowski space 177
Mirror image 213
Mirror Symmetry 10
Momentum operator 155
Momentum operator linear 93
Momentum vector 168 193
Multiplication group 12
Multiplication of linear transformations by a number 298
Multiplication of vector by a number 295 298
Multipole electric 149
Multipole magnetic 149
Multipole moment operators 150 241
Multipole radiation 147 240
Multipole wave function 149
Negative energy solutions 205
Neutrino 199 237
Nilpotent 299
Non-Abelian group 14
Norm of vectors 302
One-cycle 17
Operator 297
Operator identity 298
Operator invertible 299
Operator null 298
Operator vector 115
Order of a group 13
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