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

Hypersurface form of Kerr's theorem      216 219
Hypersurface twistors      212 215 390
I ( $N \times N$ unit matrix)      441
I, II, D, III, N, O (Petrov types)      225
I, J (Weyl scalars)      235
Identity in epsilon spinors      5
incidence      63 64 138 308 310 461
Incidence (orthogonality) of twistors      63 310
Index raising and lowering      5
Index raising and lowering for N-dimensional spinors      449
Index shifting with epsilon spinors      5
Index shifting with epsilon spinors in N dimensions      449
Index staggering for spinors      5 51
Index staggering for twistors      51
Indices, abstract and numerical      4 5
Infinitely long generators of $\mathscr{I}^{+}$       367
Infinity (conformal)      291 347 see
Infinity (conformal) for cosmological models      332
Infinity (conformal) for Minkowski space      292
Infinity (conformal) for Schwarzschild space      348 349
Infinity (conformal), $\mathscr{I}$ , $\mathscr{I}^{\pm}$ , i^{0}, $i^{\pm}$       292 348
Infinity (conformal), asymptotics of $\Omega$       362
Infinity (conformal), generators, infinitely long      367
Infinity (conformal), interpretation of null angle      377
Infinity (conformal), null angle      371
Infinity (conformal), rays don't touch it      358
Infinity (conformal), shear structure      384 388
Infinity (conformal), strong conformal geometry      369
Infinity (conformal), strong conformal geometry and infinity twistors      374
Infinity (conformal), weak equality at $\mathscr{I}$       354
Infinity for anti-de Sitter space      336 353
Infinity for de Sitter space      336 353
Infinity for FRW (Friedmann — Robertson — Walker) models      334
Infinity for Minkowski space      291
Infinity for Schwarzschild space-time      347
Infinity for space-time      291 292
Infinity twistor      66 67 97
Infinity twistor for (anti-) de Sitter space      337
Infinity twistor for anti-de Sitter space      337
Infinity twistor for de Sitter space      337
Infinity twistor for two-surface twistor      404
Infinity twistor for two-surface twistor at $\mathscr{I}$       410 411
Infinity twistor functions for cosmology      340
Infinity twistor, local twistor description at $\mathscr{I}$       376
Infinity twistor, relation to strong conformal geometry      374
Infinity twistors for Minkowski space      66 339
Initial data on null hypersurface      40
Inner (scalar) product of twistors      49
Inner product of twistors      49
instantons      (129)
Integrability conditions      90 117 see
Integral of differential form (p-form)      17
Integrals for angular momentum, twistor      75
Interpretation of null angle      377
Invisibility of Lorentz contraction      177
Irreducibility of Clifford algebra      443
Irreducibility of tensors and spinors      9 10
Irreducibility under Lorentz group      10
Isenberg, J.      (164) 168
Isomorphism (local) of groups      66 (233) 303 304 317
Isotropic medium (perfect fluid)      290
Jackiw, R.      126
Jacobi (geodesic deviation) equation      182
Jacobi field      182 209
Jacobowitz, H.      215
Janis, A.I.      425
Jeffryes, B.P.      110 400 403 408
Jordan normal form      241 (285)
Jordan normal form, specialization scheme      242
Jordan, P.      191
K (complex curvature)      27
Kelly, R.M.      401 407
Kerr coordinates      198
Kerr space-time      107
Kerr's lemma      198
Kerr's theorem      189 200 206 212 (215)
Kerr, R.P.      198 (199)
Killing equation, vector      84 93 104 396 397
Killing equation, vector, complex Killing vector      88 108
Killing equation, vector, conformal      55 72 82 101 397
Killing equation, vector, conformal, null      72 318
Killing equation, vector, defines particle constants      104
Killing equation, vector, in $\mathbb{M}(\mathscr{L})$       422
Killing equation, vector, relation to conservation laws      84 97
Killing spinor      106 118 205
Killing spinor for Kerr space-time      107
Killing spinor for Schwarzschild space-time      107
Killing spinor for type (22), vacuum      107
Killing spinor, determines propagation of polarization      107
Killing tensor      105
Killing — Yano tensor      110 111
Kinematic twistor      71 see
Kirchhoff — d'Adhemar (generalized) formula      41 330 365
Kirchhoff — d'Adhemar (generalized) formula at $\mathscr{I}$       427
Klein correspondence (representation)      307
Klein — Gordon equation      40
Klein, F.      (308)
Ko, M.      129 (217) (310) 389
Kobayashi, S.      192 193
Kodaira      (160)
Kohn, J.J.      213
Komar, A.      395 (407)
Kozameh, C.N.      127
KOZARZEWSKI, B.      394
Kramer, D.      108 126 (199) 223 277
Kristian, J.      185
Kronecker delta      5
Kronheimer, E.H.      296 297
Kuiper, N.H.      298 (302) 303
Kundt, W.      195
Labelling set      4
Lagrange identity      184
Lagrangian 2-plane      188
Lang, S.      (291)
Laplace equation      (139) see
Laplace equation, 6-dimensional      463
Law, P.      (164)
Lawson, h.b., jr.      441
LeBrun, C.R.      (164) 215 217
Left-(right-)flat      129 164 390
Left-(right-)flat, conformally      129 (310)
Lemaitre universe      336
Lewy, H.      221 222
Lichnerowicz, A.      191
Lie bracket      16 135 174
Lie derivative      16 174
Lie derivative of spinors      101
Lie derivative of spinors, relation to twistor theory      103
Lie, S.      (210) (308)
Light cone      1
Light cone of $\mathbb{M}^{#}$ as 4-plane section      303
Light cone of point $\mathscr{I}$       296 297 377 378
Light cone, caustics, crossing regions on      385
Lind, R.W.      (128) 389 421
Linear gravity (linearized general relativity)      38 163
Linear gravity (linearized general relativity) and angular momentum      422
Linear limit of Kerr space-time      109 204 205
Linear limit of Schwarzschild space-time      205 331
Lobachevski (hyperbolic) 3-space      332
Local twistors      127 131 209
Local twistors, local twistor transport      132
Local twistors, local twistor transport, Tod's 3-surface version      (406)
Logarithmic terms, elimination of      362
Lorentz group      (233)
Lorentz group as factor group of BMS group      383
Lorentz group, inhomogeneous      see "Poincare group"
Lorentz transformation      2 84
Lorentz transformation and BMS group      382
Lorentz transformation and spin-transformation      14
Lorentz transformation, effect on GPNDs      227 228

Lorentz transformation, null rotation      15
Lorentz transformation, principal null directions of      15
Lorenz gauge      32 80
Ludvigsen — Vickers mass-positivity proof      424 (431) 433
Ludvigsen, M.      129 (310) 389 424 430 433
Ludwig, G.      223 265 277
Luminosity parameter      179 184
MacCallum, M.A.H.      68 71 91 108 126 131 (139) (149) (199) 223 277
Magnetic and electric parts of Weyl (conformal) tensor, spinor      406
Magnon (— Ashtekar), A.      (353) 429
Majorana spinor (N-dimensional)      459 460 463
Manifold-with-boundary      291 297
Manin, Yu.I.      (164)
MARIOT, L.      191
Mass      110 see momentum"
Mass, ADM mass      404 429 430
Mass, Bondi — Sachs mass      415 423
Mass, positivity arguments      423
Mass, positivity arguments for gravitational wave energy      424
Mass, positivity arguments, Ludvigsen — Vickers      433
Mass, positivity arguments, Schoen — Yau      424
Mass, positivity arguments, Witten      429
Massive particle      70 74 104
Massless $\lambda\phi^{4}$ theory      332
Massless field equations, twistor equation in compacted spin-coefficient (GHP)      26
Massless free field      22 26 37 75 112 119 130 207 see "Linear "Gravitational
Massless free field and SFRs      189
Massless free field and structure of $\mathscr{I}$       352 358
Massless free field in compacted formalism      26
Massless free field in compacted formalism, conformally invariant      37
Massless free field, algebraically special      190 191
Massless free field, contour integral formulae      113 139 204
Massless free field, contour integral formulae, derivative      147
Massless free field, contour integral formulae, reversed helicity      145 146
Massless free field, Dirac — Weyl case      17
Massless free field, Maxwell case      33
Massless free field, null      13 190 (206)
Massless free field, spin-lowering      75
Massless free field, spin-raising      79 80
Massless particle      68
Maunder, C.R.F.      231
Maxwell theory      32 (139) see
McCarthy, P.J.      (380)
McLenaghan, R.G.      111
McLennan, J.A., Jr.      38
Merkulov, S.A.      (133)
Messmer, J.      389 421
Metric sphere, functions on      29
Metzner, A.W.K.      179 185 350 (396) 415 (424)
Michelsohn, M.L.      441
Milne universe      336
Milnor, J.      328
Minkowski 3-space for abreast rays      187 (299)
Minkowski 3-space for abreast rays, compactified      188 189
Minkowski coordinates      1 46
Minkowski space      1 45
Minkowski space as portion of Einstein cylinder      293 333
Minkowski space for 2-surface twistors      419 420
Minkowski space, compactified      297 316
Minkowski space, compactified and complexified      305
Minkowski space, compactified as quadric, in $\mathbb{P}^{5}$       300
Minkowski space, complex      64 139 149
Minkowski space, complex, for 2-surface twistors      408 418
Minkowski space, higher-dimensional      462 463
Minkowski tetrad      6 7
Minkowski vector space      1
Misner, C.W.      404 405 407 428 429
Modulus of elliptic curve      288
Moment sequences      91
Momentum 4-vector      68 85
Momentum 4-vector for linear gravity      75 395
Momentum 4-vector in asymptotically flat space      391 392 413
Momentum 4-vector in general relativity      395
Momentum 4-vector, quantized      142 143
Momentum 4-vector, role in twistor quantization      144 see "Rest-mass"
Monopole harmonics      (29) see
Morrow, J.      (160)
Motivation for cohomology      153
Multilinear map      4
Multiple point of curve      269
Multiplicities of GPNDs (gravitational principal null directions)      223 237
Multiplicities of GPNDs (gravitational principal null directions) and fingerprints      (232) 233
Multiplicities of GPNDs (gravitational principal null directions), tensor form      224
Multiplicity      see also "PND" "GPND"
Multiplicity of curve on $\mathbb{C}S^{+}$       268
Multiplicity of point      269
Murray, M.K.      464
N-dimensional spinors      440
N-dimensional twistors      463
n-twistor internal symmetry group      74 148
Neri, F.      461
Nester, J.M.      430 432 437
Neutrino (Dirac — Weyl) equation      17
Newlander — Nirenberg theorem      214
Newlander, A.      214
Newman — Penrose (NP) constants      427
Newman — Penrose (NP) formalism      17 22
Newman — Unti (NU) group      368 369
Newman — Unti metrics      350
Newman's $\mathscr{H}$ -space      129 389
Newman, E.T.      (29) 44 126 127 (128) 129 180 197 (217) (310) 350 358 359 369 389 390 (391) 394 (396) 420 421 423 (424) 425 427 428
News function      386 425
Newtonian potential energy      397 405 406
Nijenhuis tensor (expression)      (214)
Nirenberg, L.      213 214 215
Node      269 277 286 290
Node, isolated      278 281 282
Nomizu, K.      192 193
Non locality of gravitational energy      398 427
Non-analytic SFR (shear-free ray congruence)      201 221
Non-linear graviton      164 168 390
Norm on 2-surface twistor space      403 404
Normal subgroup of BMS (Bondi — Metzner — Sachs) group      382
NP (Newman — Penrose) constants      427
NP (Newman — Penrose) formalism      17 22
NULL      56 313
Null 2-plane      3
Null 2-plane, totally null      64 309 see beta-plane"
Null angle      371
Null cone      1
Null cone in $\mathbb{R}^{6} (=\mathscr{K})$       301
Null conformal Killing vector      72 318
Null congruence      169
Null convergence condition      (283) 289 351 426
Null datum      40 41
Null datum and energy flow      365 426 427
Null datum at $\mathscr{I}$       365
Null flag      3 8 101
Null geodesic      169 see
Null hyperplane      63
Null hyperplane, associated with massless particle      70
Null hypersurface      28 179
Null hypersurface at infinity      292 349 354
Null hypersurface in Ludvigsen — Vickers argument      (431) 433
Null massless fields      13 190 191 (206)
Null massless fields, electromagnetic      14 190 191 257 258
Null massless fields, gravitational      45 225 254 255
Null rotation      15 254
Null straight line      58
Null straight line, complex      113
Null symmetric spinor      13 14 see
Null twistor      56 313
Null vector (complex)      8 266 308 452
Null-flag bundle      3
Nullity of infinity (conformal)      353 367
Numerical indices      4
O (2,4)      66
O (space-time origin)      1 45
O(n), O(p, q), Pin (n), Pin (p, q)      (440)
Octonians (Cayley numbers)      461 462

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