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| Barut A.O., Raczka R. — Theory of Group Representations and Applications |
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| Предметный указатель |
Hilbert — Schmidt theorem 169 655
Hilbert, D. 83 169 430 524 649 655
Hirai, T. 436 577
Holman 248 312 313
Homeomorphism 53 63
Homotopic paths 60
Homotopy classes 61
Horocycle 467
Hurst, C.A. 386
Hurwitz, W.A. 71
Ideal of an algebra 1
Imprimitivity system 494 583 584 586
Imprimitivity theorem 495 582 590
Ince, E.L. 451
Induced unitary representation(s) of topological group(s) 475—476 205—213
Induced unitary representation(s) of topological group(s) and multiplier representations 484—485
Induced unitary representation(s) of topological group(s) induced by direct sum of representations 487
Induced unitary representation(s) of topological group(s) induced by nonunitary representation 571
Induced unitary representation(s) of topological group(s) of  511—512
Induced unitary representation(s) of topological group(s) of semidirect product 503—512 544 547—548
Induced unitary representation(s) of topological group(s) of semidirect product, classification of 510—511
Induced unitary representation(s) of topological group(s) of semisimple Lie groups 555—559 205—213
Induced unitary representation(s) of topological group(s) of SL(2,C) 571—574
Induced unitary representation(s) of topological group(s) of SL(2,R) 480—484
Induced unitary representation(s) of topological group(s) of SL(n,C) 560—564
Induced unitary representation(s) of topological group(s), conjugate 487
Induced unitary representation(s) of topological group(s), decomposition of tensor product of irreducible 547—548
Induced unitary representation(s) of topological group(s), induction-reduction theorem 541—542
Induced unitary representation(s) of topological group(s), irreducibility and equivalence of 495—500
Induced unitary representation(s) of topological group(s), monomial 476 507
Induced unitary representation(s) of topological group(s), of Poincare group 486—487 551 517—521
Induced unitary representation(s) of topological group(s), of Poincare group, explicit realization of 522—524
Induced unitary representation(s) of topological group(s), quasi regular 476
Induced unitary representation(s) of topological group(s), realization in terms of left cosets 485—487
Induced unitary representation(s) of topological group(s), reciprocity theorem for finite groups 549 552
Induced unitary representation(s) of topological group(s), reciprocity theorem for topological groups 550
Induced unitary representation(s) of topological group(s), tensor product theorem 546
Integrability criterion for a Lie algebra 349
Internal symmetry algebras 43
Intertwining operator 141 144
Invariant vector space 20
Irreducible group representations 146 200 225—228
Irreducible group representations of an abelian group 159
Irreducible group representations of GL(n,C) 295—298
Irreducible group representations of O(n) 287
Irreducible group representations of Poincare group 517—527
Irreducible group representations of SL(2,C) 377 571—574
Irreducible group representations of SL(n,C) 560—576
Irreducible group representations of SO(n,C) 301 308—309
Irreducible group representations of SO(p,q) 448—459
Irreducible group representations of SU(1,1) 377
Irreducible group representations of SU(3) 282—283
Irreducible group representations of U(n) 277—285
Irreducible group representations of U(p,1) 371
Irreducible group representations of U(p,q) 365—372
Ismagilov, R.S. 574
Isospin and superselection rules 405
Isotopic spin states distribution 185—187
Iwasawa decomposition of a semisimple real Lie algebra 41—42
Iwasawa, K. 41 42 100 104
Jahn, H. 274
Janner, A. 636
Janski 231
Jezuita, K. 375
John, F. 326
Joos, H. 635
Jordan, P. 417
Jost, R. 627
Kakutani, S. 71 109
Karpelevic, F. 470
Kato, T. 387
Kemmer, N. 631 635
Killing form 12—16 230
Killing, V. 12 13 14 15 46 106
Kirillov, A.A. 272 553
Kisynski, J. 358
Klein, F. 188 394 603 608
Kleinert, H. 636
Klimyk, A.U. 231 236 274
Koosis, P. 195
Kostant formula for weight multiplicities 231
Kostant — Steinberg formula for weight multiplicities 235
Kostant, B. 230 231 235 552 553
Kotecky, R. 358
Kunze, R. 157
Lanczos, C. 418 591
Landau, L.D. 635
Laplace — Beltrami operator 302 303 305 441 444 447 448 449 450 456
Laplace — Beltrami operator, spectrum of, for SO(p,q) 451—454
Laplace, P.S. 302
Lebesgue theorems 639
Lebesgue, H. 57 58 639
Lee, B.W. 635
Leja, F. 71
Levi decomposition 19
Levi — Malcev decomposition 99
Levi — Malcev Theorem 19 37 99 113 225
Levi, E. 19 37 98 99 100 113
Leznov, A.N. 195 436 577
Lie algebras 1
Lie algebras of a compact Lie group 109
Lie algebras of inner derivations 92
Lie algebras of the Lie group 86
Lie algebras radical of 18
Lie algebras, abelian 1
Lie algebras, adjoint 9 91
Lie algebras, automorphism of 6 8 13 91
Lie algebras, automorphism of, involutive 6 31 33 34
Lie algebras, Cartan decomposition 39—41
Lie algebras, Cartan metric tensor 13 16 17
Lie algebras, Cartan — Weyl basis 23—24
Lie algebras, Casimir operators 251—254
Lie algebras, center of 1
Lie algebras, centralizer 48
Lie algebras, classification of simple complex 20—29
Lie algebras, classification of simple real 29—36 47
Lie algebras, compact 16 17 32 39
Lie algebras, complex 1 14
Lie algebras, complex extension of 3
Lie algebras, complex, real form of 4 14 34—36
Lie algebras, conjunction 6 7 41 32
Lie algebras, contraction 44—46
Lie algebras, de Sitter 45
Lie algebras, derivation of 7
Lie algebras, dimension of 2
Lie algebras, direct sum of 5 8
Lie algebras, Dynkin diagrams 24—29
Lie algebras, exponential mapping 111—113
Lie algebras, full complex linear 4
Lie algebras, Galilean 46
Lie algebras, Gauss decomposition 37—39
Lie algebras, homomorphism of 6
Lie algebras, homomorphism of, natural 6
Lie algebras, ideal of 1 14 18
Lie algebras, invariant operators 251—254
Lie algebras, isomorphism of 6
Lie algebras, isomorphism of, local 90
Lie algebras, Iwasawa decomposition 41—42
Lie algebras, kernel of homomorphism 6
Lie algebras, Killing form 12—16 23
Lie algebras, Levi decomposition 19
Lie algebras, Levi factor 19
Lie algebras, Levi — Malcev theorem 19 37 99
Lie algebras, nilpotent 11 12 37—38
Lie algebras, noncompact 16
Lie algebras, orthogonal 4
Lie algebras, orthogonal, symmetric 126
Lie algebras, quotient 5 6 18
Lie algebras, real 1 14 19—36 39
Lie algebras, representation of 9
| Lie algebras, representation of, adjoint 9
Lie algebras, representation of, in a Hilbert space 318
Lie algebras, representation of, in a Hilbert space, domain of 320 322
Lie algebras, representation of, in a Hilbert space, Garding subspace 321 324
Lie algebras, representation of, in a Hilbert space, integrability criterion 349 355 357 358
Lie algebras, representation of, in a Hilbert space, skew adjoint 319
Lie algebras, representation of, in a Hilbert space, topologically irreducible 319
Lie algebras, root system 20—28
Lie algebras, semidirect sum of 8 9
Lie algebras, semisimple 15 17 19 253
Lie algebras, simple 16 19
Lie algebras, simple roots of 23 24
Lie algebras, simple, dimension of 29
Lie algebras, so(4,2) 51
Lie algebras, solvable 11 12 16 17 37—38
Lie algebras, structure constants 2
Lie algebras, structure theorems 18—19
Lie algebras, subalgebra 1
Lie algebras, subalgebra, Cartan 20 21 37 38
Lie algebras, symplectic 4 35
Lie algebras, Weyl basis 3
Lie product 80
Lie theorem 200
Lie transformation group 87—88
Lie, S. 1 4 80 81 86 87 90 114 200
Lifting criterion 402
Limic, N. 313 445 453 455 457 470 577
Lipsman, R. 577
Localizable relativistic system 581—584
London, G.W. 314
Loomis, L. 130 132
Lorentz group 513—515
Lorentz group connection with SL(2,C) 514—515
Lorentz transformations 39
Lorentz, H.A. 513 514 515
Lunn, M. 591
Macfarlaine, A.J. 229
Mackey decomposition theorem 70 473 481
Mackey, G.W. 70 130 131 153 154 489 501 536 549 550 551 552 553 591
Majorana, E. 611 612 634
Malcev, A.I. 19 37 98 99 100 113
Manifold, analytic 76—77
Manifold, analytic, complex 76
Manifold, differentiable 75
Manifold, topological 75
Maschke, E.K. 189
Maurin, K. 155 163 275 373 470 640 652 655 658
Maurin, L. 373 470
Mautner, F.I. 153 154 552
Maxwell, J.C. 291
McGlinn, W.D. 48
Measurable vector fields 655
Measure disintegration theorem 131 132
Measure, Borel 637 639
Measure, Haar 67—70 73 74 420 423
Measure, Haar for SL(2,C) 68
Measure, invariant on a group 67 71
Measure, invariant on Lie groups 109—110 450
Measure, invariant on Lorentz group 444
Measure, Plancherel 421 422 427 435—436
Measure, quasi invariant on homogeneous spaces 130
Measure, Radon — Nikodym theorem 639
Measure, spectral 652
Measure, spectral canonical 583
Measures, tensor product of 639
Melsheimer, O. 373 592
Meltzner 525
Messiah, A. 346
Metric 53—54 72 73
Metric invariant on a group 71
Metric invariant on homogeneous spaces 126
Metric invariant on Lie groups 111
Metric space 53—54
Metric space, compact 57 58
Michel, L. 629
Mickelson, J. 358 372
Micu, M. 263
Miller, W. 313 437
Minimal coupling 613
Montgomery, D. 71 83 84
Moore, C.C. 552
Moser, W.O.J. 196
Moshinsky, M. 195 274
Multiplication, Lie 1
Muzinich, I.J. 635
Nachbin, L. 71 113 195
Nagel, B. 358
Nagy, B.Sz. 664
Naimark, M.A. 158 160 163 436 437 501 552 570 573 574 575 577
Nambu, Y. 635
Nelson operator A 327 422 428
Nelson, E. 317 322 324 327 332 343 345 348 357 372 373 428 434 588
Newton, T.D. 591 593
Nghiem Xuan Hai 437
Niederer, U.H. 635
Niederle, J. 313 358 372 445 453 455 457 470 577
Nikodym, O.M. 130 562 563 639
Nikolov, A.V. 370
Noether, E. 266 637
Norton, R.E. 635
Nuclear space 442
Nuclear spectral theorem 658—659
O'Raifeartaigh, L. 635
Operator valued distribution 460 461 465
Operator(s) tensor, contravariant 243
Operator(s) tensor, contravariant, irreducible 244
Operator(s), absolute value of 333—337
Operator(s), adjoint 642—643
Operator(s), analytic dominance 337—344
Operator(s), bounded 323 641 643
Operator(s), closed 641—642
Operator(s), closure of 642
Operator(s), commutativity criterion 351
Operator(s), continuous 641
Operator(s), decomposable 657
Operator(s), deficiency index 644 664
Operator(s), diagonal 657
Operator(s), elliptic 327 341 359 428
Operator(s), essentially self-adjoint 663—665
Operator(s), Hilbert — Schmidt 655
Operator(s), intertwining 141 144
Operator(s), invariant, on homogeneous spaces 439—441
Operator(s), Nelson,  327 422 428
Operator(s), positive definite 641
Operator(s), self-adjoint 643—644 649 652
Operator(s), self-adjoint, extension of 643 664
Operator(s), self-adjoint, function of 662—663
Operator(s), symmetric 641 643—644 663—664 665
Operator(s), tensor, covariant 244
Operator(s), unbounded 323
Orbit of a character 505
Ore, O. 267 637
Orsted, B. 501
Osima, M. 552
Ottoson, U. 288 312 371
Oxtoby, J.C. 71
Pajas, P. 236 313 470 471 472
Parastatistics 298
Parity and superselection rules 406
Parseval 174 658
Parseval equality 174 442 658
Particle, elementary 525
Particle, unstable 531
Particle, unstable, description of 531—534
Particle, unstable, scalar 534—535
Particle, unstable, with spin 535—536
Pauli, W. 417 418 591 630 634 635
Perelomov, A.M. 260 273
Peter — Weyl theorem 174
Peter — Weyl theorem, generalized 426
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