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Barut A.O., Raczka R. — Theory of Group Representations and Applications
Barut A.O., Raczka R. — Theory of Group Representations and Applications



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Название: Theory of Group Representations and Applications

Авторы: Barut A.O., Raczka R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1980

Количество страниц: 717

Добавлена в каталог: 30.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $H^{2}(G,K)$      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 $S_{n}$      188
Group(s), topological      61 82
Group(s), topological of transformations on $\Gamma$      123
Group(s), topological of transformations on $\Gamma$, effective      123
Group(s), topological of transformations on $\Gamma$, 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 $E_{n}$ and $\pi_{n}$      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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