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| Barut A.O., Raczka R. — Theory of Group Representations and Applications |
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| Предметный указатель |
Abers, E. 635
Adler, S. 274
Ado theorem on Lie algebras 10
Ado, I.D. 10
Algebra of intertwining operators 144
Algebra, von Neumann 658
Algebras, Lie see "Lie algebras"
Ambrose, W. 160 163
Analytic manifold 76—77
Analytic manifold complex 76
Analytic manifold product of 77
Analytic structure 76
Analytic vector field 79
Analytic vector(s) 322
Analytic vector(s) dense set of 332 364
Analytic vector(s) for a group representation 322
Analytic vector(s) for a Lie algebra 335 344 352—353
Analytic vector(s) for an operator 331
Analytic vector(s) for unitary representation of Lie group 344 345
Anderson, R.L. 314 371 470 579
Angelopoulos, E. 588 591
Antiunitary operators 403
Araki, H. 158
Auslander, L. 195 522
Bacry, H. 636
Baird, G.E. 312
Baker — Hausdorff formula 587
Baker, G.A. 588
Balaban, T. 375
Bargmann, V. 314 402 418 501 605 619 625 635
Barut, A.O. 314 386 387 388 391 635 636
Bateman, H. 418
Bayen, F. 588 591
Beltrami, E. 302
Berezin, F.A. 275 314 470
Berger, M.S. 128 132
Bernat, F. 552
Bertrand, J. 591
Bhabba, H.J. 631 635
Bichteler, K. 197
Biedenharn, L.C. 248 274 312 313
Biharmonic coordinate system 303
Biharmonic coordinate system on hiperboloid 449 456
Birkhoff, G. 71 109 250
Blattner, R.J. 501
Bochner, S. 163
Bolzano, B. 57 58
Bondi, H. 525
Borel isomorphism 638
Borel map 638
Borel measure 638
Borel space 638 640
Borel subsets 638
Borel, A. 57 58 70 131 638
Boson operators 310
Bruhat criterion V 446
Bruhat, F. 105 120 446 501 557 577
Cartan decomposition of a semisimple real Lie algebra 39
Cartan metric tensor 13
Cartan subalgebra 20 230
Cartan — Weyl basis 23 24 229
Cartan — Weyl communication relations 23—24 229
Cartan, E. 13 19 20 23 34 39 40 46 47 94 100 103 104 106 114 132 470
Cartier, P. 373
Casimir operators for classical Lie groups 254—266
Casimir operators for classical Lie groups for semisimple Lie groups 273—275
Casimir operators for classical Lie groups, generating function for the spectrum of 257 273
Casimir, H. 252 254 259 273 328
Cattaneo, U. 636
Cerulus, F. 196
Chacon, P. 195
Character of an abelian group 159
Character of an irreducible representation of simple Lie group 236—237
Character of an irreducible representation of simple Lie group, compound 192
Character of an irreducible representation of simple Lie group, primitive 192
Chart 75 82
Chevalley, C. 19 114 253 275
Chow, Y. 637
Clebsch — Gordan coefficients 150 182—184 236 247 465
Clebsch, A. 150 182 232 236
Coester, F. 48
Coherent states 396
Coherent subspaces 396
Cohomology group  624—625
Combe, Ph. 636
Compact metric space 57 58
Completeness relation 428
Component of a point of a topological space 60 64
Composition functions of a group 82
Concrete linear space 396 412
Conformal group 409
Conformal group, generators of 412
Conformal invariance of relativistic equations 413
Contraction of Lie algebras 44—46
Convergence 53
Convergence, strong 54
Convergence, weak 55
Coupling, minimal 612
Covering group 70
Coxeter, H.S.M. 196
Creation and annihilation operators 309
Cunningham, E. 418
CYCLE 188
Dashen, R. 274
de Sitter, W. 45
de Swart, J.J. 236
Deficiency index of an operator 644 664
Differentiable manifold 76
Differentiable structure 76
DIN 274
Dirac, P.A.M. 314 417 418 601 602 608 634
Distance in metric space 53
Dixmier, J. 158 373 437 552 577 578
Doebner, H.D. 373 592
Dominated Convergence Theorem 639
Dual object of a group 159
Duality theorem of Pontriagin 163
Duffin, R.G. 631 635
Dunford, N. 638 644
Dynkin diagrams 24—29
Dynkin, E.B. 12 13 20 24 27 28 46
Eckart, C. 247 274
Edmonds, A.R. 236
Einstein, A. 291
Elementary particle 525
Elementary systems associated with space-time transformations 524—525
Elliot, T. 274
Emch, G. 418
Engel, F. 114
Enveloping algebras 249—251 258
Enveloping algebras, representation by unbounded operators 323—331
Enveloping algebras, representation by unbounded operators, selfadjoint element of 325—330
Enveloping algebras, representation by unbounded operators, symmetric element of 324—325 326
Enveloping field of a Lie algebra (Lie field) 266 270
Equivalence relation 637
Euclidean group 431
Euclidean group, generalized 431 440
F-space 638
Factor system 623
Fedoseev, I.A. 195 577
Feit, W. 192
Fermion superselection rule 404
Fierz, M. 630 635
Fischer, J. 313 470 577
Flato, M. 352 357 373 587 591
Fock, V.A. 314
Fourier transform, generalized 420 423
Frame, J.S. 192
Frechet and Riesz theorem 640
Frechet, M. 640
| Freudenthal theorem 230
Freudenthal, H. 46 230 231
Frobenius reciprocity theorem 549 552
Frobenius, G. 191 500 549 550 552
Fronsdal, C. 314 635
Fubini — Tonelli theorem 462 639
Fubini, S. 640
Function on a topological group 61
Function on a topological group, uniformly continuous 66
G-module 622
Galilean algebra 45—46
Galilean group 91
Gantmacher, F.P. 31 34 47
Garding subspace (domain) 321 324 329 331 344 422 424
Garding, L. 314 317 320 321 322 364 372 373 424 496 588
Gauss decomposition of a Lie algebra 37—39
Gauss decomposition of a Lie group 100—103 206 233
Gauss, C.F. 37 38 100 103 559
Gel'fand — Chevalley theorem 275 302
Gel'fand — Kirillov theorem on the generators of enveloping field 272
Gel'fand — Zetlin pattern m 279
Gel'fand, I.M. 154 195 236 272 275 277 279 3J2 313 371 372 421 436 437 466 470 501 570 574 575 577 609 613 635 658
Gerfand triplet 655 395 421
Gindikin, S.G. 470
Ginibre, J. 274
Girardello, l. 391
GJazman, I.M. 654 663
Gleason, A. 59
Gleasons theorem on local compactness 59 64
Godement, R. 160 163 238 313 470
Golodetz, V.J. 314
Goodman, R. 373
Gordan, P. 150 182 232 236
Gordon, W. 603 608
Graev, M.I. 195 312 371 372 470 577
Gramm, J. 120
Grodsky, I.T. 635
Group(s) 61
Group(s) of causal automorphisms in Minkowski space 408
Group(s) of conformal transformations in Minkowski space 409
Group(s) of conformal transformations in Minkowski space, generators 412
Group(s) of symmetry 409
Group(s) of type I 145 155 420 536
Group(s), alternating AN 191
Group(s), covering 70
Group(s), cyclic 145
Group(s), extension of 620
Group(s), extension of, central 622
Group(s), extension of, classification 622—625
Group(s), Galileo 91
Group(s), GL(n,R) 62
Group(s), Haar measure for 67—70
Group(s), Haar measure for, connected 65
Group(s), Haar measure for, homogeneous 63
Group(s), Haar measure for, isomorphism of 63
Group(s), isotropy 473
Group(s), Lie 81—82 83
Group(s), Lie and Lie algebras 86—89
Group(s), Lie, adjoint 91 251
Group(s), Lie, analytic subgroup of 84
Group(s), Lie, automorphism of 91
Group(s), Lie, Bruhat decomposition of 105
Group(s), Lie, Cartan decomposition of 103—104
Group(s), Lie, Casimir operators of 254—266
Group(s), Lie, classical, connectedness of 108
Group(s), Lie, commutant of 99
Group(s), Lie, commutator of 99
Group(s), Lie, compact connected 109
Group(s), Lie, direct product of 95
Group(s), Lie, Gauss decomposition of 100—103 206 223
Group(s), Lie, Iwasawa decomposition of 104 272
Group(s), Lie, Levi — Malcev decomposition of 99
Group(s), Lie, Levi — Malcev theorem 100 113 225
Group(s), Lie, local isomorphism of 90
Group(s), Lie, locally euclidean 83
Group(s), Lie, minimal parabolic subgroup of 105
Group(s), Lie, nilpotent 99
Group(s), Lie, one parameter subgroup of 84
Group(s), Lie, semidirect product of 96 503 536
Group(s), Lie, semisimple 99
Group(s), Lie, simple 99
Group(s), Lie, simple, classification of 106—108
Group(s), Lie, solvable 98
Group(s), Lie, structure constants 85
Group(s), little 473
Group(s), Lorentz 513—515
Group(s), Lorentz, connection with SL(2,C) 514—515
Group(s), orthogonal 62 64
Group(s), Poincare 97 515—516
Group(s), Poincare, generalized 426
Group(s), realization of 137
Group(s), simply reducible 182
Group(s), simply reducible, compact 246
Group(s), SL(2,C) 514—515 564 567 571—574
Group(s), SL(n,C) 559—560
Group(s), SO (4,2) 409
Group(s), SO(p,q) 448—456
Group(s), stationary 473
Group(s), symmetric  188
Group(s), topological 61 82
Group(s), topological of transformations on  123
Group(s), topological of transformations on , effective 123
Group(s), topological of transformations on , transitive 123
Group(s), topological, infinite-dimensional 83
Group(s), topological, locally compact 84
Group(s), topological, locally euclidean 83
Group(s), topological, locally separable 130
Group(s), topological, subgroup of 62
Group(s), topological, subgroup of, central 65
Group(s), topological, subgroup of, invariant 62
Group(s), topological, subgroup of, normal 123
Group(s), unimodular 69
Group(s), universal covering 70
Gruber, B. 236
Gupta, S.N. 187
Gurcvich, A.V. 195
Haar measure 67—70 73 74 420 423
Haar, A. 67 68 69 70 71
Hagen, C.R. 229
Hamel basis 137
Hamel, G. 165
Hamermesch, M. 48
Harish-Chandra 313 373 436 437 466 470 577
Harmonic analysis on  and  432
Harmonic analysis on abelian groups 421—423
Harmonic analysis on compact groups 423
Harmonic analysis on homogeneous spaces 438 441—446
Harmonic analysis on semidirect product groups 431—435
Harmonic analysis on symmetric spaces of pseudoorthogonal group 446—456
Harmonic analysis on unimodular groups 423—429
Harmonic analysis, Harish-Chandra and Helgason theory 466—470
Harmonic functions 302 303
Hausdorff space 55 58
Hausdorff space, locally Euclidean 75
Hausdorff, F. 67 71 156 163 438
Hausner, M. 34 36 47 48
Heat equation on a Lie group 358
Hecke, E. 470
Hegerfeldt, G.C. 48
Heine, W. 165
Heisenberg commutation relations 588
Heisenberg commutation relations, Weyl form of 588—589
Heisenberg field 270 272
Heisenberg, W. 238 267 272 417 418 466 468 469 470 581 588 591
Helgason, S. 21 23 24 36 90 94 104 108 113 114 132 275 441
Hennig, J. 48
Hewitt, E. 67 71 156 163 438
Hilbert spaces, direct integral of 656
Hilbert spaces, direct sum of 143
Hilbert — Schmidt operator 655
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