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

Differential form (p-form) on $\mathscr{N}$       209
Differential form (p-form), basis 1-forms      17 437 438
Dighton, K.      127
Dirac (electron) equation      40
Dirac (electron) equation, n-dimensional      462
Dirac (— Clifford) matrices      441
Dirac (— Fierz) higher spin equation      40
Dirac 4-spinor      (47) 437 460
Dirac operator for 3-space      431
Dirac — Weyl (neutrino) equation      17 434
Dirac — Weyl (neutrino) equation, n-dimensional      462
Dirac, P.A.M.      (29) 66 (302) 303
Disphenoid      249
Distance (interval) in Minkowski space      1 67
Divergence of ray congruence      177 see
Division ring (field)      12 95
Dodson, C.T.J.      135
Dolbeault cohomology      (160)
Dominant energy condition      424 436 437
Double curve      268 286 289 290
Double point      269 277 286 290
Double point, isolated      278 281 282
Dray, T.      (29) 422
Dual basis for twistors      50
Dual of angular momentum twistor      87
Dual of exact sequence      91
Dual of form      39 98
Dual of module      4
Dual of Riemann tensor      19 20
Dual of skew $\gamma$ -matrix product      444 445
Dual of skew twistor      65
Dual of tensor      11 12 14 39
Dual of twistors, skew      65
Dual twistor      48 310 311 313
Dual twistor correspondence      313
Dual twistors      48
Dual, duality between angular momentum twistor and Killing vector      101
Duality rotation      21
Duals of anti-symmetric (skew) tensor      77 12 14 444 445
Duals of exact sequences      91
Dyad      6 17
Eastwood, M.G.      78 119 (124) 148 (149) (164) 325 326 464
ECSK (Einstein — Cartan — Sciama — Kibble) theory      (184)
Eddington — Lemaitre universe      336
Eddington, A.S.      126
Edth      23 see
Effect on GPNDs (gravitational principal null directions) of Lorentz transformation      227 228
Ehlers, J.      191
Ehrenpreis, L.      152
Eigenbivectors of Weyl (conformal) tensor, spinor      242
Eigenspinors of Weyl (conformal) tensor, spinor      233
Eigenvalues of Weyl (conformal) tensor, spinor      235
Eigenvalues, eigenvectors of Ricci spinor (trace-free Ricci tensor)      277
Eightfold periodicity for N-dimensional spinors      447
Einstein cylinder (static universe)      294 295 329 332
Einstein cylinder (static universe), anti-Einstein universe      333
Einstein energy-loss formula      425
Einstein field equations      20 22 164 169 192 352 354 437
Einstein — Maxwell (electrovac) theory      33 34 198 290 354 406 407
Einstein — Maxwell (electrovac) theory, asymptotic expansion      364 393
Einstein — Maxwell (electrovac) theory, peeling property      358 364
Einstein — Maxwell (electrovac) theory, scalar invariants      263 264
Einstein, A.      425
Electromagnetic (Maxwell) field tensor, asymptotic behaviour      393
Electromagnetic (Maxwell) field tensor, conformal weights      39
Electromagnetic (Maxwell) field tensor, null      14 190 191 257 258
Electromagnetic (Maxwell) field tensor, peeling property      358 364
Electromagnetic (Maxwell) field tensor, purely electric, magnetic      33 257 258
Electromagnetic (Maxwell) field tensor, spinor      32 255
Electrovac equations      33 see
Elementary state      150 152
Elliptic curve      288
Ellis, G.F.R.      108 182 (207) (283) 296 297 335 336 338 436
Energy (-momentum) tensor for Dirac — Weyl field      39
Energy (-momentum) tensor for electromagnetic field      33 85 290 426
Energy (-momentum) tensor for massless scalar      126
Energy (-momentum) tensor for massless scalar, 'new improved'      125
Energy (-momentum) tensor in linear gravity      38 99
Energy (-momentum) tensor, physical      289 290
Energy (-momentum) tensor, trace-free      85 352 353 409
Energy of gravitational wave, radiation      397 (406) 426
Energy positivity conditions      283 289 351 424 426 436 437
Energy tensor for Dirac — Weyl (neutrino) equation      39
Energy tensor for electromagnetic (Maxwell) field tensor      33
Energy tensor for neutrino (Dirac — Weyl) equation      39
Energy tensor for Weyl (Dirac — Weyl) neutrino equation      39
Energy tensor in linear gravity (linearized general relativity)      38 99
Energy-momentum      see "Momentum 4-vector"
Epsilon spinors      5
Epsilon spinors for asymptotic spin space      417 418
Epsilon spinors for asymptotic spin-space      417 418
Epsilon spinors, N dimensional      445 447
Epsilon twistor      54 see
Equations for electromagnetic (Maxwell) field tensor      33 39
Equianharmonic      3 237 276
Eth ( $\partial$ )      23
Eth ( $\partial$ ), conformally invariant      36 37
Euler homogeneity operator      141 (211) 272
Euler homogeneity operator as twistor helicity operator      144
Exact sequence for massless free field      116
Exact sequence for twistor equation      118 119
Exact sequence for two-surface twistor      417
Exact sequences      89 116
Exact sequences for 2-surface twistor      417 423
Exact sequences for massless free field      116
Exact sequences for symmetric twistor equation      118 119
Exact sequences, (Poincare —) de Rham      90
Exact sequences, Koszul      95
Exact sequences, moment sequence      95
Exact sequences, periodic moment sequence      91
Exact sequences, sheaf exact sequence      (90) 117
Exact sequences, twistor-space Poincare structure      91
Exact set (of interacting fields)      40
Exterior calculus, fundamental theorem of      17 28
Exterior derivative      16
Exterior product      16
Exton, A.R.      428
Extrinsic curvature of 2-surface      400
Extrinsic curvature of 3-surface      406
Farrar, G.      461
Fefferman metric      (217)
Fefferman, C.      (217)
Field (division ring)      12 95
Field, M.      152
Fierz — Pauli condition      37 120
Fierz, M.      (29)
Fingerprint of $S^{+}$ (anti-celestial sphere) and Weyl spinor      229
Fingerprint of Weyl (conformal) tensor, spinor      229
Fingerprint of Weyl tensor      229
Flag path      3 320
Flag plane      8 170
Flag plane and phase of twistor      70
Flag plane and Weyl tensor fingerprint      229
Flag-plane field of $\omega^{A}$       322
Flagpole      2 8
Flagpole field of $\omega^{A}$       59 72
Flaherty, E.J., Jr.      (128) 201
Floyd, R.      109
Fluid, perfect      290 347
Foliation      169
Folland, G.B.      213
FORM      16 444 see
Form, symmetric 'form'      260
Forward tube      152 154 316 345
Four-valuedness of twistors      316
Friedmann Universe      335 336 343
Friedrich, H.      366 368
FRW (Friedmann — Robertson — Walker) models      228 229 332
FRW (Friedmann — Robertson — Walker) models, conformally flat      229
Fundamental observer(galaxy)      (334) 335 336

Fundamental theorem of exterior calculus      17 28 76 98
Fundamental theorem of exterior calculus on null hypersurface      37
Further rescaling of infinity (conformal)      370 371
Further rescaling of infinity (conformal) to flatness      392 393
Future causal      (74) 427
Future end-point      296
Future null vector      8
Future set      296
Future tube      152 see
Future-asymptotically simple      353 367 428
Future-endless      297
G (gravitational constant: notation change from volume 1!)      20
Galaxy (fundamental observer)      335 336
Gamma-plane      453 457 460
Garding, L.      45 81
Gauge freedom of potential for angular momentum twistor      71 101
Gauge freedom of potential for exterior derivative      90
Gauge freedom of potential for Killing vector (twistor)      88
Gauge freedom of potential for massless field      79 119
Gauge freedom of potential for Ward function      167
Gauge freedom of potential for Yang — Mills      34 168
Gauss — Bonnet theorem      27
Gaussian curvature      27 374 387 400 401 404
Gegenbauer function      (29)
General coordinate group      366
Generator of $\mathbb{C}\mathscr{I}^{+}$       422
Generator of $\mathscr{K}$       301
Generator of null hypersurface      180 181
Generator of quadric      267
Generators of null hypersurface      180
Genus      27
Geodesic      (169) 170
Geodesic deviation (Jacobi) equation      182
Geodesic distance in anti-de Sitter space      340
Geodesic, null      see "Ray"
Geodetic      60 (169) see "SFR"
Geodetic distance in (anti-) de sitter space      340
Geodetic distance in de Sitter space      340
Geometry of contour integrals of twistor functions      148
Geometry of Weyl (conformal) tensor, spinor      246
Geroch — Held — Penrose (GHP) formalism      23 see
Geroch, R.P.      296 297 351 353 367 421
Gibbons, G.W.      (129)
Gilkey, P.B.      399
Gindikin      (164) (308)
Ginsberg, M.L.      (149)
GL(n, $\mathbb{C})$ (general linear group)      165
Godemont, R.      161
Goldberg — Sachs theorem      195
Goldberg, J.N.      195
Good cut      384
Googly graviton      (164)
GPND of Schwarzschild space-time      229 231
GPNDs (gravitational principal null directions)      190 223
GPNDs (gravitational principal null directions) and $\mathbb{C}S^{+}$       267
GPNDs (gravitational principal null directions) and EPNDs      264
GPNDs (gravitational principal null directions), addition theorem      226
GPNDs (gravitational principal null directions), harmonic and equianharmonic      237
GPNDs (gravitational principal null directions), representation on $S^{+}$       226
GPNDs (gravitational principal null directions), specialization scheme (Penrose diagram)      226
Grace, J.H.      258 260 264
Gradient      15
Grassmann, H.      (308)
Gravitational constant      20
Gravitational energy      see also "Bondi — Sachs mass" "Quasi-local
Gravitational energy of radiation      426
Gravitational energy, potential      397 405 406
Gravitational field      see also "Linear gravity" "Massless
Gravitational field at infinity (conformal)      358
Gravitational field, algebraically special      191 224
Gravitational field, conformal scaling as spin-2 field      357 358 386
Gravitational field, null      45 225 254 255
Gravitational field, radiation fields      364 388
Gravitational spinor      20 see
Gravitational wave, radiation      390 391 424 426 427 429
Gravitational wave, radiation, back-scattered      429
Gravitational wave, radiation, plane      126
Graviton      163 164
Graviton, googly      (164)
Graviton, non-linear      164 168 390
Green, P.      (164) 168
Grgin behaviour      328
Grgin behaviour of massless free field      329
Grgin behaviour of Ward, construction, conformally invariant      329 330
Grgin index      316 327
Grgin index of electromagnetic (Maxwell) field tensor      329
Grgin index of gravitational field      331
Grgin index of primary spinor part of twistor      328
Grgin theorem      329
Grgin, E.      329
Griffiths, P.      152 160 161 162
Grothendieck, A.      95
Gunning, R.C.      161 165
h, $\zeta$ , g (components of connecting vector)      175
Handedness of Robinson congruence      60 61 314
Handedness of spin structure, spinor structure of $\mathbb{M}^{#}$       319
Hansen, R.O.      44 129 (310) 404
Harmonic, cross-ratio      3 237 239 276
Harmonic, spherical, spin-weighted      29
Harris, J.      152 160 161 162
Harvey, F.R.      459
Hausdorff (non-Hausdorff)      (207)
Hawking, S.W.      108 (129) 182 (207) (283) 296 297 335 336 338 416 436
Helicity of massless field      37 152
Helicity of massless field, raising and lowering      80 147
Helicity of massless particle      69 314
Helicity of twistor      56 69 134 322
Helicity, quantized      144 145
Herlt, E.      108 126 (199) 223 277
Hermann, R.      169
Hermiticity of quasi-local energy-momentum/angular momentum expression, quasi-local angular momentum twistor      403
Hertz-type potential      81
Hicks, N.J.      182 184
Higher-valent twistors      50
Higher-valent twistors, dependence on position      53
Higher-valent twistors, local twistors      134 135
Higher-valent version of twistor equation      54 55 77 see
Hirzebruch, F.      161
Hitchin, N.J.      44 (129) 390
Hodge*-operation (dual)      11 12 14 39 65 445
Hodge, W.V.D.      452
Hodges, A.P.      148 (149)
Hoermander, L.      222
Holomorphic coordinates      128 214
Holomorphic coordinates for 2-surface      27
Holomorphic cross-section of bundle      165 326 390
Holomorphic curve      390
Holomorphic function      128 (191) 201 212 see
Holomorphic function of twistor      113 139 144 199 202
Holomorphic function on complex manifold      214
Holomorphic functions of twistors      113 140—144 199 202
Holomorphic tangent space      214
Holomorphic twistor theory      326
Homogeneity of twistor function      113 140
Homogeneity of twistor function and Grgin index      332
Homogeneity, degree      113 140 141 144
Homomorphism of groups      66 (233) 303 304 317
Hopf fibring      61
Hopf, H.      61
Horizon of Schwarzschild space-time      351
Horizons for FRW (Friedmann — Robertson — Walker) models      335 336
Horizons of black hole      351
Horizons, cosmological      335 353
Horowitz — Perry mass-positivity proof      434
Horowitz, G.T.      351 367 424 430 431 434
Huggett, S.A.      44 68 148 (149)
Hughston, L.P.      (74) 95 97 108 (109) 110 145 148 (149) (161) (302) 463
Hurd, T.R.      95 97 (149) (302) 340
Hyper-Minkowski space      462 463
Hyperbolic (Lobachevski) 3-space      332

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