Penrose R., Rindler W. — Spinors and space-time. Spinor and twistor methods in space-time geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Penrose R., Rindler W. — Spinors and space-time. Spinor and twistor methods in space-time geometry

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Название: Spinors and space-time. Spinor and twistor methods in space-time geometry

Авторы: Penrose R., Rindler W.

Аннотация:

Spinor and Twistor Methods in Space-Time Geometry introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. Twistors have, in recent years, attracted increasing attention as a mathematical tool and as a means of gaining new insights into the structure of physical laws. This volume also includes a comprehensive treatment of the conformal approach to space-time infinity with results on general-relativistic mass and angular momentum, a detailed spinorial classification of the full space-time curvature tensor, and an account of the geometry of null geodesics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Repr

Год издания: 1988

Количество страниц: 512

Добавлена в каталог: 26.03.2011

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Предметный указатель

Spinorial object      3 317 440
Spinors, irreducible (totally symmetric)      10
Spinors, N-dimensional      440
Spinors, N-dimensional, pure      451
Spinors, N-dimensional, reduced      66 440 443
Splitting off skew indices      6
Staggering of indices      5 51
Stark, R.F.      108
Stationary space-time      385 (391) 428
Stein manifold      161
Stephani, H.      108 126 (199) 223 277
Stereographic coordinate (complex)      1 2 31 356 368
Stewart, J.M.      368
Streubel, M.      395 421 422
Strong conformal geometry      369 see
Strooker, J.R.      89
Structure of spin-space, N-dimensional      454 455
SU (2,2) (twistor group)      67 316
Supersymmetry      (45) 463
Supertranslations      381
surface      see "Null hypersurface" "Spacelike "Spacelike
Surface area form on infinity (conformal)      375
Surface-area 2-form      27 28
Surface-area 2-form on $\mathscr{I}$       375
SW-(Sen — Witten) equation      430
Symmetric spinor      10 13 39 40 233
Symmetric spinor, Hermiticity      275
Symmetric spinor, null      13
Symmetric spinor, positivity      283 289 290
Symmetric tensor      10 11
Symmetric tensor, trace reversed      11
Symmetric tensor, trace-free      10 11
Symmetric twistor      55 75 111 147
Symmetry group      see also "Individual groups"
Symmetry group of particular Maxwell tensors      258 259
Symmetry group of particular Weyl tensors      249
Symmetry operations      8
Symplectic structure      211
Synge, J.L.      68 395
Syzygy      263 264
Tableau symmetry      9 10
Tacnode      269 280 281 284 286 290
Tafel, J.      222
TAMBURINO, L.A.      421
Tamm, Ig.      (29)
Taub, A.H.      131
Taubes, C.H.      430
Tensor algebra      3
Tensor translation of spinor algebra      10
Tensor translation of spinors      10
Tensor, anti-symmetric      11 12 14
Tensor, symmetric      10 11
Tensor-spinor correspondence      5
Tensor-spinor correspondence, n-dimensional      450
Tensor-spinor correspondence, translation symbols      8
Terrell, J.      177
Tetrad, Minkowski      6 7
Tetrad, null      6 7
Thompson, A.      195
Thorn ( $\mathfrak{p}$ )      23
Thorn ( $\mathfrak{p}$ ), conformally invariant      36 37 41
Thorne, K.S.      405 407 428
Thorpe, J.A.      231
Three-surface twistor      406
TIPs and TIFs      297 335 353 354
Tod form of quasi-local expression      (401) 405 432
Tod, K.P.      44 68 127 129 (310) 347 389 390 394 401 404 405 406 407 408 (421) 424 430 432 434
Tolman universe      336 344 347
Tolman, R.C.      336
Topology for 2-surface-twistor surface      399
Topology of $\mathbb{P}\mathbb{T}^{\pm}$ , $\mathbb{P}\mathbb{N}$ , $\mathbb{T}^{\pm}$ , $\mathbb{N}$       (313)
Topology of $\mathscr{I}^{+}$ $\mathscr{I}^{-}$       349 354
Topology of compactified Minkowski space      299 300
Topology of null geodesic      314
Torsion      15 (184) 437 438
Trace-free energy tensor      85 352 353 409
Trace-free twistor      54 55 78 83 87 95 96 111 147 397
Transition function      162
Translation between tensors and spinors      5 10
Translation between tensors and spinors in n dimensions      450
Translation symbols      8
Translations      381
Transvection      13
Trautman, A.      126 350
Treves, F.      215
Triple point      269 284
Turnbull, H.W.      (285)
Twist of bundle      324
Twist of ray congruence      61 177
Twist of ray congruence, twist-free congruence      179 207 (210)
Twistor contour integral for wave function for massive particle      148
Twistor contour integral for wave function for massless particle      139
Twistor description of light cone      64 65
Twistor diagram theory      (149)
Twistor equation      26 43 44
Twistor equation in compacted formalism      26
Twistor equation in compacted formalism, 2-surface twistor equation      399
Twistor equation in compacted formalism, conformally invariant      37
Twistor equation in n dimensions      463
Twistor equation in tensor form      77 396
Twistor four-valuedness      316
Twistor function      113 139 202
Twistor geometry      58 305
Twistor group      67 316
Twistor norm for two-surface twistor      403 404
Twistor norm for two-surface twistor at $\mathscr{I}$       416 417
Twistor quantization      142
Twistor quantization of helicity      144
Twistor solution of Ward, construction      139 150 151
Twistor solution of Ward, construction, higher-dimensional      463
Twistor space      46 see
Twistor space, ambitwistor space      (164)
Twistor theory      viii 43 44 65 189
Twistor theory and Kerr's theorem      viii 200 202
Twistor theory, higher-dimensional      viii 462 463
Twistor theory, holomorphic      viii 326
Twistor theory, twistor particle programme      viii 74
Twistor wave function      143 see
Twistor wave function, massive      148 162

Twistor wave function, massless      139 160
Twistor wave function, n particles      161 162
Twistor wave function, non-linear      162
Twistor-real skew twistors      67 95 339
Twistors      43
Twistors, alternating twistors      54 65 408
Twistors, asymptotic      212 389 390
Twistors, bang and crunch      342
Twistors, flagpole field      59 72
Twistors, global      131
Twistors, Hermitian      55 71 83 136 397
Twistors, hypersurface      212 215 390
Twistors, independence of origin      48 49
Twistors, left-, right-handed      56
Twistors, multiplication by scalar      47
Twistors, N-dimensional      462 463
Twistors, reason for name      61
Twistors, skew      54 55
Twistors, skew, simple      65 66 341
Twistors, skew, to represent points      65 305
Twistors, skew, twistor-real      67 95
Twistors, symmetric      54 55 75 111 147
Twistors, trace-free      54 55 78 83 87 95 96 111 147 397
Two-surface twistor      395 396 398 see "3-surface
Two-surface twistor for $\mathscr{L}$ at $\mathscr{I}$       408
Two-surface twistor, alternating twistor      408
Two-surface twistor, associated complex Minkowski space      408 418
Two-surface twistor, associated real Minkowski space      419 420
TYPE      23
Type of weighted quantity      23
Types of Weyl (conformal) tensor, spinor      225
Uncontorted 2-surface      400 401 406 408 412 421
Uncontorted 3-surface      406
Universal covering space      304 338
Universe radius function      346
Unphysical metric      291 368
Unti, T.W.J.      350 369 394 (424)
Urbantke, H.      (308)
Vacuum space-times      107 108 195 223 347 348 352 354 366 389 427 437 see
Valence      10
Valence of twistors      51
van der Burg, M.G.J.      179 185 350 (396) 415 (424)
Vanishing of Weyl tensor at infinity (conformal)      356
Veblen, O.      61 131 (308) 441
Vector bundle      see "Bundle"
Vickers, J.A.G.      424 430 433
w (conformal weight)      29
Wald, R.M.      85 108 336 435
Walker, M.      107 108 110 (350) 368 (430)
Walker, R.J.      269 288
Ward, construction      164 see
Ward, construction for Maxwell field in curved space      126
Ward, construction for Weyl spinor      126
Ward, construction, conformally invariant      82 124 125
Ward, construction, explicit procedure      166
Ward, construction, wave equation      39 81 82
Ward, R.S.      43 44 68 (74) 78 164 (310) 390 464
Wave function      142
Wave function for massive particle      40
Wave function for massless particle      26 37 39 124 see
Wave-front, asymptotically plane      377 378
Weak asymptotic simplicitly      351 353
Weak energy condition      (283) 289 351 426
Weak equality      354 see
Weak-field limit of general relativity      38 see
Weighted quantity      23
Weinberg, S.      347
Weizenboeck relations      125
Wells, R.O., Jr.      43 44 68 78 148 152 (160) 325 326
Wess — Zumino (twistor) equation      463
Wess, J.      (45) 463
Weyl (conformal) tensor of symmetry groups of degeneracy (PND coincidence)      255 256
Weyl (conformal) tensor, spinor      20 137
Weyl (conformal) tensor, spinor degeneracy (PND coincidence)      see "GPNDs multiplicities
Weyl (conformal) tensor, spinor, asymptotic behaviour      393
Weyl (conformal) tensor, spinor, canonical forms      239
Weyl (conformal) tensor, spinor, curvature covariants      258 260
Weyl (conformal) tensor, spinor, not massless field scaling      357 358 386
Weyl (conformal) tensor, spinor, peeling property      359 360 364
Weyl (conformal) tensor, spinor, representation on $S^{+}$       226
Weyl (conformal) tensor, spinor, symmetries in special cases      251
Weyl (conformal) tensor, spinor, vanishing at $\mathscr{I}$       356
Weyl (conformal) tensor, spinor, vanishing implies conformal flatness      137
Weyl (Dirac — Weyl) neutrino equation      17 434
Weyl (Dirac — Weyl) neutrino equation, n-dimensional      462
Weyl, H.      441
Wheeler, J.A.      405 407 428
Whittaker, E.T.      (139)
Will, C.M.      (350) 368
WINICOUR, J.      421
Witten mass-positivity argument      398 424 429 438 461
Witten, E.      (164) 168 398 424 429 430 436 437
Witten, L.      263
Woodhouse, N.M.J.      128 (160) 188 211 328 401
World-line      70 204
World-line of particle      70
World-tensor      5
World-tensor as spinor      5
Wu, T.T.      (29)
Yamabi equation      332
Yang — Mills (YM) theory      34 35 (133)
Yang — Mills (YM) theory, (anti-) self-dual      35 164
Yang — Mills (YM) theory, general fields      168
Yang — Mills (YM) theory, Quasi-local charge integral      (401)
Yang — Mills (YM) theory, YM-charged field      34 164 165
Yang, C.N.      (29)
Yasskin, P.      (164) 168
Yau, S.-T.      424 429
Young tableau      9 10 81 82
Young, A.      258 260 264
Young, J.W.      61 (308)
z ( $\zeta, \overline{\zeta}$ vector)      183
Z (ray for null twistor)      58
Zero rest-mass free-field equations      26 see
Zumino, B.      (45) 463
[U, V] (Lie bracket)      16
{ } (varying over $\mathscr{S}$ )      (399)
{1111}, {211}, etc. (GPND coincidences)      225
{p, q} (type): p = r'-r, q = t'-t      23
{r', r; t', t} (type)      23

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