|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Gilmore R. — Lie Groups, Lie Algebras and Some of Their Applications |
|
|
|
| Предметный указатель |
Inner product of roots 280 281 287—290 302 303
Inoenue — Wigner contraction 446—450 471 487 492 493 504
Inoenue, E. 446 506
int 320 321 323 333 501
Integrability conditions 101 103
Integration 57 78—85
Interchanges 11
Internal degrees of freedom, quantum system 55
Intersection 45 58 59
INTO 18
Invariance principles 145
Invariant 145 223
Invariant density 79—81
Invariant integral 78—84 395—397
Invariant integration 84
Invariant measure 209 319 391—401
Invariant metric tensor 434
Invariant subalgebra 142 223 224 234—236 251 254 255 258—261 263 308 449 468—470 477
Invariant subgroup 72 74 86 87 94 180 225 320
Invariant subspace 223 230 231 233 244 245 248 265 474
Invariant volume 80—83 391—401
Invariant volume element 79 80
Inverse 1 3 5 14 68 69 93 97 320
Inverse function theorem 36
Inverse image 60
Inverse in continuous group 64
Inverse in continuous group of transformations 65
inversion 20
Involutive automorphism 318 337 338 340 344 408—411 422
IO(2) 210
Irrational 328—330
Irreducible 110 138 236 346
Irreducible representation 110 232 402 484
ISO(2) 210 212 443 445 478 494
ISO(3) 83 85 243 247 428 493
ISO(3), regular representation 243
ISO(3, 1) 83 457 493
ISO(4) 457
ISO(n) 118 452 453 479—481
ISO(p, q) 83 452 453 457 481 491 493
Isometries, group of 492
Isometry 478
Isomorphic 7
Isomorphic linear vector spaces 7
Isomorphic, globally 85 110
Isomorphic, locally 85 110
Isomorphic, topologically 85
Isomorphism 14 18 22
Isomorphism among classical groups 52
Isomorphism, analytic 151 152
Isospin 121 145 146
Isotropic harmonic oscillator 423—425
Iterated solution, Taylor’s theorem 117
Iteration 114—115
IU(n) 481
IU(n, f) 86
IU(p, q) 83 482 491 493
IUSp(2p, 2q) 83 483 491
j 275
J (field) 18
Jacobi identity 10 104—106 118 224 266 267 322 486 489 491 492
Jacobi polynomials 54
Jacobi polynomials, contracted limit of 495
Jacobi polynomials, generating function for 180
Jacobson, N. 23 277 317 435
Jordan canonical form 218 241—243 254 473—474
Judd, B.R. 317
K (complex conjugation operator) 183 185 201
K (field) 18
Kaehlerian manifold 378 484
Karpelevic, F.I. 435
Kernel 480 482
Killing, W. 277
Kleima, D. 277 317
Klein — Gordon hamiltonian 429 430
Kobayashi, S. 506
Kramer, P. 435
Kronecker product 28
Kupczynski 472—477
Kupczynski, M. 477 506
L 23 275
Lagrangian 145
Laguerre polynomials 54
Laplace — Beltrami operator 357 358 362 433 495
Larmor frequency 163—166 176 177
Lattice equilibrium site 498
Left coset 73 201
Left half-plane 71 72
Left invariant density 80
Left invariant integral 84
Left invariant measure 79 80 81
Left translation 79—83 92
Legendre polynomials 54
Legendre polynomials, associated 181
Legendre polynomials, contracted limit of 495
Legendre polynomials, generating function for 181
Lehner, J. 435
Length 388
Level 300 305 316
Levi decomposition 261
Levi — Civita tensor 274
Lexigraphic order 301
Lichnerowicz, A. 56
Lie algebra 9 10 16 87—229 144
Lie algebra and root spaces 216—277
Lie algebra, real forms of 422
Lie bracket 105 224
Lie derivative 105
Lie group 63 77 84 87—229
Lie group of transformations 77 87—91 102 103
Lie group, canonical composition function 94
Lie group, semidirect product 158
Lie group, semisimple 158
Lie group, simple 158
Lie group, solvable 158
Lie, S. v 86 108
Lie’s first theorem 96—97 101
Lie’s first theorem, converse 106 107
Lie’s second theorem 100—103
Lie’s second theorem, converse 107
Lie’s theorems 87 228 229—234 244 263 304
Lie’s theorems, converses 87 107—108
Lie’s third theorem 104 105
Lie’s third theorem, converse 108
Lift 127
Light cone, forward 85
Limit points 60 77
Limits of integration, change of 116
Line element 431 432 498 499
Linear 262 266
Linear algebra 8 10 237
linear combination 6
Linear constraint, in algebra 403
Linear dependence 6
Linear difference 269
Linear differential operator 5
Linear function 245
Linear independence 6 157
Linear independence of simple roots 303 304
Linear integral operator 6
Linear superposition 12
Linear transformation 114 218 219 237
Linear vector space 5 6 10 11 16 19 85 93 106 115
Linear vector space, representation for 18
Linearization 110 144 217
Linearly dependent 6
Linearly independent 6 93 266
Little Prince 436—443 478
ln 110
Local analytic isomorphism 107 114
| Local change of basis 107
Local continuous group 76 77
Local coordinate system 41 61 62
Local Lie group 77 107
Local Lie group of transformations 107
Local properties, of continuous group 76
Local property 94
Local quantity 145
Locally compact 77 85
Locally Euclidean 61 62
Locally isomorphic 76 110
Loebl, E.M. 349
LOG 110
Logarithm 15
longitude 133 389
Loomis, L.H. 86
Loops, in Dynkin diagram 308 309
Lorentz group, homogeneous 85
Lorentz group, inhomogeneous 83 453
Lorentz group, measure on 401
Lower indices 39
Lower triangular 54 139 157 158 297 298
Magnetic field 162 165 166 176 177
magnetic moment 162
Magnetic moment, anomalous 162
magnetization 176
Magnus, W. 23
Major diagonal 40 42
Malkin, I.A. 349 435
Manifold 68 69 71 73 76 84
Manifold, differentiable 61
Manifold, dimensionality of 62 63
Man’ko, V.I. 349 435
Mapping 13 18 19 22 78
Mapping into 18
Mapping onto 18
Mapping, canonical 94
Mapping, injective 18
Mapping, noncanonical 94
Mapping, surjective 18
Maradudin, A.A. 506
Mass-1 light cone 379
Mathematical analysis, relation with group theory 36
Matrix 12
Matrix addition 6 8 15
Matrix algebra, and Jacobi identity 104—105
Matrix elements 100 147 148 179 319
Matrix elements  180
Matrix elements for \mathfrak{su}(2) 140
Matrix elements of  140 155
Matrix elements of  139—141 155
Matrix elements, representations of SU(2) 137 153 155 156 158
Matrix groups 24—56
Matrix groups, infinitesimal generators for 92—94
Matrix invariants 248
Matrix multiplication 2 8 9 13 22 69 94 106
Matrix representation 15 19 20 69 70 105—106 217 223 266 350 351 353 354
Matrix representation of U(2) 136—141 153—157 460—462
Matrix representatives for  294 297
Matrix representatives for  297
Matrix representatives for  297
Matrix representatives for  297
Matrix representatives of simple roots 300
Matrix transpose 22 41
Matrix, antisymmetric 9
Matrix, block diagonal 195 213
Matrix, column of 12
Matrix, diagonal 22 302
Matrix, hermitian 16 22
Matrix, identity 9 23
Matrix, nonsingular 2 23
Matrix, off diagonal 195 213
Matrix, Pauli spin 17
Matrix, row of 12
Matrix, symmetric 9
Matrix, unitary 16
Maximal abelian subgroup 328
Maximal compact subalgebra 213 318 319 332 337 338 340 341 346 348
Maximal compact subgroup 200 201 257 420
Maximal solvable invariant subalgebra 225 234 235 255 256 258
Maximal subalgebra 319 408—411 422
Maximal subgroup 83 158 492 493
Maximality axion, for manifolds 61
Maxwell’s equations 349
Measurable 147
Measure 57 78—85 319 391—401
Measure on a coset 385—391
Measure on classical groups 395—401
Measure on cosets 391—395
Measure, antisymmetric 38—42
Measure, bilinear 38—42
Measure, Cartan — Killing 248—249
Measure, definite 407
Measure, degenerate 250 253
Measure, indefinite 407
Measure, multilinear 276
Measure, nonsingular 38—42
Measure, positive definite 38—42
Measure, r-linear 276
Measure, sesquilinear 38—42
Measure, symmetric 38—42
Metric 37—53 213 248—255 319 324 325 327 329 331 354
Metric in function space 43
Metric tensor 390 431—434 483 485 486 488
Metric tensor, inverse 483 485 486 488
Metric-preserving group 24 37—53 118 183 197 199
Michel, L. 181
Miller, W. x 23 86 119
Minimal polynomial 243
Minkowski space 377 378
Minkowski, R. 43
Minor diagonal 42 341 344
MOD 222 223 225 227 229—231 233 244 256—258 274 305
Modulus 15 50
Momentum operator 461
Moshinsky, M. 435
Multilinear metric 276
Multiphoton mode algebra 494
Multiple commutator 297 298
Multiple integral, in a group 396
Multiplication group 94
Multiplication matrix 94
Multiplication, pointwise 21
Multiply connected 108 110 134 334 427
Mutually commuting generators 240
n-tuple 87 88
Nagel, J.G. 506
Negative root 298—300
Negative-definite 251 257 327 329—331 333
Neighborhood 35 36 49 76—78 353
Ne’eman, Y. 506
Nilpotent 227—229 238 241 244 245 250 254—258 264 274
Nilpotent algebra 229 317 505
Nilpotent group 477
Nilpotent Lie group 83
Nilpotent matrix 229 465 473
Nomizu, K. 86 506
Non-Euclidean spaces 36
Nonassociative algebra 219 274
Noncanonical mappings 94
Noncanonical parameterizations, of SU(2) 149—151 153 158
Noncommutative group 4
Noncompact 113 330 338 341—343
Noncompact algebra 200
Noncompact generators 185 186 195 200 412—419 421
Noncompact real form 421
Noncompactness 16
Noncosmological limit 457
Nonlinear constraint, in a group 403
Nonlinear normalizing condition 266
|
|
|
| Реклама |
|
|
|
|
|
О проекте