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

Bonnor, W.B.      (396) 427
Boost      2
Boost, infinite      227 365 366
Boost-weight      23 29
Bramson, B.D.      411 421
Brauer, R.      441
Bryant, R.L.      217 464
Buchdahl condition      37 see
Buchdahl, N.P.      119
Bundle      34 164 see
Bundle of (abreast) rays      177 187 207
Bundle, local twistor      132
Bundle, spin-vector      3 437
Bundle, twistor spin-bundle over $\mathbb{M}^{#}$       324
C(1,3), $C^{\uparrow}_{+}(1, 3)$ (conformal groups)      300
Callan, C.G.      126
Canonical decomposition      13
Cantoni, V.      (380)
Cartan, E.      67 131 223 441 462
Carter's constant      110
Carter, B.      110 111
Causal      (74)
Causal boundary      295
Causal curve      296
Caustic      385 (299)
Cayley numbers      461 462
Cayley, A.      (308)
Cech cohomology      155
Celestial sphere      2
Chandrasekhar, S.      (29) 108 110
Charge integral for Maxwell field      76
Charge integral for Maxwell field in twistor form      (149)
Charge integrals for electromagnetic (Maxwell) field tensor      76 77
Charged fields      32 45
Chern, S.      160 165 231
Chevalley, C.      441 461
Churchill, R.V.      265 277
Classification by coincidence of matrix eigenvalues      241 242 277 278 (283) 285 286
Classification of $\Omega_{ABC^{'}}$       268
Classification of electromagnetic (Maxwell) field tensor      255 257
Classification of general symmetric spinor      265
Classification of general symmetric spinor, categories      282
Classification of general symmetric spinor, Hermiticity      274
Classification of general symmetric spinor, positivity      275
Classification of Maxwell tensor, spinor      255 257
Classification of Ricci spinor (tensor)      265 275 286
Classification of Ricci spinor (tensor), categories      282
Classification of Ricci spinor (tensor), positivity      283
Classification of symmetric spinor      265
Classification of vectors      274 275
Classification of Weyl tensor, spinor      223 see spinor"
Clifford (— Dirac) equation      441
Clifford algebra      442
Clifford multiplication      444
Clifford parallels      61
Clifford, W.K.      61 442
Clumped (composite) index      4
Coboundary      158 161
Coboundary operator      161
Cochain      160 161
Cocycle      157 161
Cohomology      118 139
Cohomology element with respect to covering      158
Cohomology, Cech      160
Cohomology, Dolbeault      (160)
Cohomology, group element      158 160
Cohomology, r-function      155 160
Cohomology, relative      (149)
Coleman, S.      126
Commutator equations in compacted spin-coefficient (GHP)      25
Commutator of compacted operators      25
Commutator of covariant derivatives      15
Commutator of local twistor derivatives      136
Commutator, Lie bracket      16
Commutator, spinor form      21
Commutators for eth ( $\partial$ )      25
Commutators for thorn ( $\mathfrak{p}$ )      25
Compacted spin-coefficient (GHP), basic equations      25
Compacted spin-coefficient (GHP), formalism      23 169 197 367
Compacted spin-coefficient (GHP), need for weighted scalar A      371 372
Compacted spin-coefficient (GHP), the $(\kappa, \rho, \sigma, \tau)$ 4-vector $S_{a}$       174 175 182
Compactified Minkowski space      297
Compactified Minkowski space, complexified      305
Complex ( = kind of sequence)      (89)
Complex conjugation      128 214 (284)
Complex conjugation in complexified space      128
Complex conjugation of alpha-, beta-curve      218
Complex conjugation of complex tangent vector      214
Complex conjugation of higher-valent twistors      56
Complex conjugation of local twistor      134 135
Complex conjugation of N-dimensional spinors      459 460
Complex conjugation of position vector      66
Complex conjugation of twistor      50 56
Complex conjugation of twistors      50 56 313
Complex conjugation on $S^{+}$       280
Complex conjugation on twistor space      313
Complex conjugation on twistor space, quasi-local      403
Complex curvature of 2-surface      27
complex curve      see also "Alpha- beta-curve"
Complex curve on $CS^{+}$       266
Complex curve, double curve      268
Complex geometry      64 127 266 305
Complex manifold      127 212
Complex null geodesic      311 312
Complex null vector      8 266 308
Complex orthogonal group      233
Complex point of space-time      66 128 307
Complex projective line      149 307
Complex space-time      127
Complex stereographic coordinate      1 2 31 356 368 393
Complex structure      212 see
Complex tangent vector      213 214
Complex vector space      46 441
Complex world vector      66
Complex world-line      419
Complexification of $S^{+}$       266
Complexification of $\mathscr{I}^{+}$       389 390
Complexification of Euclidean space      (64)
Complexification of Minkowski space      64 139 149
Complexification of Minkowski space, compactified      305
Complexification of ray      (64) 113 311 312
Complexification of real-analytic expression      128 129
Complexification of space-time      127
Complexified $S^{+}$ (anti-celestial sphere)      266
Components of $\gamma$ -matrices      441 442
Components of curvature spinors      22
Components of curvature, spinors      22
Components of derivatives of spinors      24
Components of dual twistor      50
Components of dual twistors      50
Components of higher-valent twistors      52
Components of tensor      4
Components of twistor      48 50 52
Components of twistors      48
Composite (clumped) indices      4
Condition for conformally flat space-time      137
Conditions for types of Weyl (conformal) tensor, spinor      260
Conformal (Weyl) tensor, spinor      20 see
Conformal compactification      188
Conformal equivalence of cross-sections      302 355
Conformal geometry      see "Conformal invariance"
Conformal geometry of $\mathscr{I}$       see "Infinity conformal"
Conformal geometry of Minkowski 3-space of abreast rays      187
Conformal group      66 67 303 316
Conformal infinity      291 347 see
Conformal invariance of $\alpha$ -plane      309 310
Conformal invariance of 2-surface twistor space      400
Conformal invariance of charge-current vector      39
Conformal invariance of hypersurface twistors      218 219
Conformal invariance of hypersurface, twistors      57 58 218 219

Conformal invariance of inner (scalar) product of twistors      57 58
Conformal invariance of invariant contact structure      218 219
Conformal invariance of local twistor theory      132
Conformal invariance of massiess free fields      38 39 359
Conformal invariance of massless free field      38 112
Conformal invariance of massless free field and Weyl spinor      357 358
Conformal invariance of primary spinor part of twistor of symmetric trace-free twistor      56 111
Conformal invariance of ray      66 172 295
Conformal invariance of SFR      197
Conformal invariance of spinor derivatives      78 111
Conformal invariance of trace-free energy tensor      38
Conformal invariance of twistor equation      45
Conformal invariance of twistor scalar product      57 58
Conformal invariance of Weyl (conformal) tensor, spinor      120 121
Conformal invariance of Weyl tensor (spinor)      120 121
Conformal Killing equation      82 see
Conformal mapping between cross-sections      302 355
Conformal mapping of cosmological model      332
Conformal motions of $S^{+}$ , $S^{-}$       2
Conformal motions of $\mathbb{M}^{#}$       316
Conformal motions of $\mathscr{I}$       366 368
Conformal motions of celestial sphere      2 368
Conformal motions of metric sphere      29 31 383
Conformal rescaling      35
Conformal rescaling for infinity      291 347 360
Conformal rescaling of curvature      120
Conformal rescaling, complex      (328)
Conformal rescaling, preserving flatness      119 123 124
Conformal weight (of conformal density)      29 36 37 132 327 358
Conformally flat space-time      45 82 111 121 137 400 401
Conformally flat space-time, right (left) conformally flat      129 (310)
Conformally invariant derivatives      111 124 see
Conformally invariant eth, thorn      36 37 41
Conformally invariant tensors, spinors      120 121 127 136 137
Congruence      169 see "Robinson
Congruence, null      170
Congruence, null, shear-free      189 see
Conjugate of twistor equation      49
connecting vector      174
Connection      15 see
Connors, P.A.      108
Conservation laws for charge      76 77
Conservation laws for linear gravity      77 97
Conservation laws, relation to (conformal) Killing vectors      84
Conserved integrals for linear gravity (linearized general relativity)      75 97 396 397
Conserved integrals for linear gravity (linearized general relativity), ten vanishing integrals      77 88 100
Consistency conditions      see also "Integrability conditions"
Consistency conditions for massiess field (Fierz — Pauli — Buchdahl — Plebanski)      37 120 191
Consistency conditions for twistor equation      45 120 130
Constant measure of twist of ray congruence      184 209
Constant spinor field      30 46 130 140
Constants for particle      104
Contact structure      211
Contact structure, conformal invariance of invariant contact structure      218 219
Contact structure, invariant contact structure      207 438
Contorted 2-surface      400 401 412
Contour integrals of twistor functions      114 139
Contour integrals of twistor functions, branched      156
Contour integrals of twistor functions, higher-dimensional      463
Contracted (inner) product      4
Convergence (divergence) of ray congruence      177
Convergence (divergence) of ray congruence, propagation of area      179
Convergence and shear of null hypersurface      181
Convergence of ray congruence      177
Coordinate basis      17 214
Coordinates, advanced and retarded      292 348 356
Coordinates, asymptotically null      392
Coordinates, Bondi retarded time      373 380 393
Coordinates, Bondi retarded time, Bondi system      386
Coordinates, complex stereographic      1 2 31 356
Coordinates, local      162 210 211 214
Coordinates, null      392
Correction factor for quasi-local energy-momentum/angular momentum expression      (401) 402 407 408
Correction factor for quasi-local energy-momentum/angular momentum expression at $\mathscr{I}$       410
Cosmological constant      20 22 108 352
Cosmological constant and structure of $\mathscr{I}$       353
Cosmological constant in quasi-local expression      (402)
Cosmological models      332
Cosmological models, description in terms of $\mathbb{P}^{5}$       337
Coulomb field      205 331
Covariant derivative      15 see
Covariants of curvature      258 260
Covering      154
Covering space      304 338
Covering, common refinement      159
Covering, locally finite      156
Cox, D.      201
Coxeter, H.S.M.      298 (302) 303
CR-function      215
CR-manifold      215
CR-structure      212 214 215
Crampin, M.J.      211
Cross-ratio      2
Cross-ratio of eigenvalues of Ricci tensor      289
Cross-ratio of GPNDs      236
Cross-ratio of PNDs of Plebanski spinor      289
Cross-sections of $\mathscr{I}$ (cut)      355 356 373 384 385
Cross-sections of $\mathscr{I}$ (cut), determine Lorentz subgroups      383 384
Cross-sections of $\mathscr{I}$ (cut), good and bad      384
Cross-sections of $\mathscr{K}$       302
Cross-sections of bundle      165 326
Crunch twistor      342
Cup product of r-function, cohomology      162
Curtis, G.E.      (71)
Curvature covariants      258 260
Curvature for local twistors      136
Curvature of 2-surface      27
Curvature spinors for complex space-time      129 130
Curvature, Gaussian      27 374
Curvature, invariants      262
Curvature, local twistor      136
Curvature, spinors      19
Curvature, spinors for complex space-time      129
Curvature, tensor      15
Curvature, tensor, Riemann (spinor form)      19
Curvature, Yang — Mills      34 35
Curve      see also "Complex curve"
Curve, casual      296
Curve, real locus on $S^{+}$       274 275
Cusp      269 279 280 286
Cut      384 see
D'Alembert equation      39 see
D, $\delta$ , D', $\delta^{'}$       18
dA (exterior derivative)      16
de Rham (— Poincare) sequence      90
De Sitter space      336 350
de Sitter space, asymptotically      350
Decomposition of twistor, angular momentum      73 74
Definiteness of angular momentum, twistor      75
Deformation of complex manifold      162
Derivative covariant      15
Derivative covariant, change of under conformal rescaling      36
Derivative of massless free field      39 40
Derivative with respect to abstract-indexed quantity      141
Derivative, directional      17 133
Derivative, local twistor      133
Derivatives of symmetric spinors in compacted spin-coefficient (GHP)      25
Deser, S.      404 429
Determinant of quasi-local energy-momentum/angular momentum expression, quasi-local angular momentum twistor      404
Dietz, W.      110
Dieudonne      95
Diffeomorphism group      366
Different kinds of complex point of space-time      314
Differential equation for primary spinor part of twistor      44 49 55 81 396
Differential equation for primary spinor part of twistor in tensor form      77
Differential equations for higher-valent twistors      53
Differential equations for spinor parts of twistors      44 46 49 53
Differential form (p-form)      16 (200)
Differential form (p-form) for surface area      27
Differential form (p-form) for twistor integral      142 342 (149)

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