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Ward R.S., Wells R.O. — Twistor geometry and field theory
Ward R.S., Wells R.O. — Twistor geometry and field theory



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Название: Twistor geometry and field theory

Авторы: Ward R.S., Wells R.O.

Аннотация:

This book deals with the twistor treatment of certain linear and non-linear partial differential equations in mathematical physics. The description in terms of twistors involves algebraic and differential geometry, and several complex variables, and results in a different kind of setting that gives a new perspective on the properties of space-time and field theories. The book is designed to be used by mathematicians and physicists and so the authors have made it reasonably self-contained. The first part contains a development of the necessary mathematical background. In the second part, Yang-Mills fields and gravitational fields (the basic fields of contemporary physics) are described at the classical level. In the final part, the mathematics and physics are married to solve a number of field-theoretical problems.


Язык: en

Рубрика: Физика/Классическая физика/Классические поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 520

Добавлена в каталог: 20.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Real-axis      355 357
Reality condition      391 416 418 419 445
Reality constraints      393
Rebbi, C.      276 278
Regular representation      128
Relative cohomology      161 355 366
Relative cohomology exact sequence      369
Relative cohomology group      356 422
Relative de Rham complex      302 307 313 340 348 382
Relative de Rham operator      303 382
Relative de Rham sequence      304 313 319 337 347 382 465
Relative exterior derivative      398
Relative forms      305 306
Relativity theory      1 3
Repeated index      129
Resolution      176 228
Restricted Lorentz group      47 60
Restricted Poincare group      60
Restriction mapping      97 167 168— 180
Ricci identity      443
Ricci tensor      286 287 288 294 440
Richard, J.L.      415
Riemann curvature tensor      286
Riemann sphere      10 62 377 380 383 384 426
Riemann surface      7 85 148 185 189 192 193 196
Riemann tensor      288
Riemann — Roch theorem      86
Riemann, B.      7
Riemannian geometry      129
Riemannian manifold      146 212 295
Riemannian metric      121 122 208
Riemannian space      294 445 457
Right-flat vacuum spaces      294
Right-handed massless fields      250 331 334
Rindler, W.      121 125 241 246 250 257 258 260 286—291 311 350 472
Ringed space      461 473 475 476—480
Rogers, A.      473
Rosenblum, P.M.      473
Rossi, P.      15 185 382 424
Rothstein, M.      473 480
Rouhani, S.      431
Salamon, S.      449
sans serif font      120
Sato's microfunctions      367
Sato, M.      367
Saveliev, M.V.      284
Scalar curvature      287 292 295 440 443
Scalar field      242 254 267 280 289 291 423
Scalar function      105 291 406
Schapira, P.      209 359
Scheme      478
Schwartz, L.      359
Schwarz, A.S.      276
Schwarzschild space      295
Second filtration      221 231
Second order differential equations      242 334 336
Section      72 74 167 355
Seifert, H.-J.      473
Self-dual complex planes      434
Self-dual complex two-planes      372
Self-dual field equations      423 459
Self-dual fields      274 387
Self-dual gauge fields      267 371 397
Self-dual gauge-field equations      397 448
Self-dual instantons      275 277 278
Self-dual Maxwell field      338 414
Self-dual Maxwell's equations      349
Self-dual monad      415
Self-dual part      249 266 273 287 293 294 312 373
Self-dual plane      372—374 434
Self-dual solutions      267 274
Self-dual space      446
Self-dual space-time      286 433 448 451
Self-dual surface      434 435 436—439 443 444 449
Self-dual two-forms      244 273 312 373
Self-duality condition      277 278 293 459
Self-duality equation      266 267 371 277 397 432
Semisimple complex groups      37
Semisimple real groups      37
Serre duality      316 317 322 338 339
Serre, J.-P.      2 166
Several complex variables      2 166 342
Sheaf      67
Sheaf cohomology      2 148 153 161 175 176 178 179 184 185 191 194 196—198 200 206 230 301 302 355
Sheaf cohomology group      182 350 383 399 404
Sheaf morphism      169 172 173 175
Sheaf theory      2 148 157 166 171
Shirokov, A.P.      46
Shirokov, P.A.      46
Shnider, S.      473 481 483 484
Short exact sequence      170 173 175 180 207 213 216 237 345
Sibner, L.M.      278
Sibner, R.J.      278
Simple poles      353
Simply-connected space      164
Singer, I.M.      86 275—278 389—391 413 445
Single-fibration picture      372 387
Singular chains      154 160
Singular cochains      159
Singular cohomology      160 161 182 184 200 232
Singular homology groups      157 160
Singular point      477 478
Singular simplex      154
Skew spinors      247
Skew-symmetric bilinear form      138
Skew-symmetric fc-fold tensor product      26
Skew-symmetric form      130
Smooth (p, q)-forms      168 171
Smooth differential forms      119 182
Smooth function      13 82 168 170 182 183 206 357
Smooth line bundles      195
Smooth manifold      39 286
Smooth mapping      74 96
Smooth maps      141
Smooth relative p-forms      328
Smooth sections      79 92 168 328
Smooth vector bundle      118 328
Smooth vector fields      93 168
SO(4)-frame bundles      215
SO(p, q)-manifold      212
Sommerfield, C.M.      284
Source-free Maxwell equations      244 245 248 249 252 255 266 279
Source-free Maxwell field      243 258
Southern hemisphere      391
Space-reflection      259
Space-time      1—3 263 267 270 279 280 286 290 293 296 398 411 433 448 449
Space-time manifolds      122
Space-time metric      267 286
Space-time picture      444
Spanier, E.H.      159
Sparling, G.A.J.      397 422
Special linear group      36
Special relativity      45 51 241 242
Special unitary groups      37 264
Spectral curve      429
Spectral sequence      2 218—221 223 225 226 228 230 231 233 234- 238 327 330—332 335—337 340 347 348
Spectral sequence mapping      236
Spectral sequences      149 196 197 202 302
Spin bundle      208 209 214 308 311 442 445 482
Spin structure      149 212 213 215 216 235 237 287 308 311 445
Spin-bundle      216
Spin-frame bundle      215
Spin-space      246 259 442 449
Spinc -bundles      215
Spinor algebra      127 308
Spinor bundle      115 125 126 127 262 302
Spinor coordinates      321 482
Spinor differential operators      319
Spinor field      125 127 245 246 260 261 301 302 311 347 349 395 406 434—436 454
Spinor frame      129 130 447
Spinor index      132 246 287
Spinor representation      338
Spinor Ricci identity      434 441
Spinor sheaves      302 308 311 344
Spinorial forms      308
Spinors      24
Split manifold      480
Splitting construction      383 387
Splitting formula      379 380
Splitting functions      394
Splitting mapping      480
Splitting matrices      402
Spontaneous symmetry breaking      281
Square-norm mapping      210
Stalk      70
Standard complex      220 225 231
Standard coordinates      22 241—243 449
Standard filtration      236 237
Standard metric      122 272 295 449
Standard simplex      152 155
Star-operator      243
Steenrod, N.      90 122 164
Stein manifold      185 342 369 370
Stereographic coordinate      428
Stereographic projection      18 272 273
Sternberg, S.      142 144
Stiefel — Whitney class      199 214
Stokes' theorem      280 282—284
Stora, R.      415
Streater, R.F.      362 367
Strong nuclear forces      263
Structure      89 140 212 218 265 269 274 416
Structure group      51 88
Structure group reduction      121
Structure sheaf      168 193 411 460 473 475 477 478 480 481
SU(2)-connection      204 393 429
SU(2)-gauge potential      421 423
SU(2)-instanton      276 371 398 417
Subbundle      75
Summation convention      129
Super conformal group      482
Super Euclidean space      475 480
Super flag manifold      482
Super Lie algebras      473
Super Minkowski space      460 483
Super null lines      483
Super Poincare group      482
Super twistor manifold      460 473 481
Super twistor space      481 482
Super vector bundles      473
Super Yang — Mills fields      460
Supercommutative rings      474 479
Superconnection      483
Superderivation      483
Supergeometry      468 472 473 479 482
Supergravity theories      472
Supermanifold      460 473 475 476 479—481 483
Supersymmetric field theories      472
Supersymmetric string theories      472
Supersymmetric theories      257 482
Supersymmetric transformations      472
Supersymmetric Yang — Mills equations      484
Supersymmetry transformations      473 482
Support      77 355
Symmetric spinor field      331 341
Symmetric spinor forms      312
Symmetric tensor algebra      120
Symmetric tensor product      75 79 116
Symplectic form      246 249 259 415- 442 444 450 452 455
Symplectic groups      391
Symplectic structure      246
Tangent bundle      12 84 92 102 115 124 138 139 146 198 208 274 308 426
Tangent plane      17 30
Tangent sheaf      483
Tangent space      12 13 15 37 47 49 51 65 73 74 140 142 445
Tangent vector      13 14 29 37 42 72 73 93 125 141 287 435 436 438 440
Tangential Cauchy — Riemann equations      360
Tangential Cauchy — Riemann structure      361
Taubes, C.H.      275 279 281 283 284 426
Taylor series expansion      38 188 339 346 461
Tensor algebra      80 115 119 208 209 308 310 311
Tensor bundles      115 208 209
Tensor field      80 116 118 260 297
Tensor product      18 19 75 79 115
Time-inversion      259
Tod, K.P.      456 458
Topological boundary      55 63
Topological charge      273 274 277 282
Topological invariant      95 96 148 149 150 153 159 162 193 197 198 214 410
Topological pullback      304 325
Topological space      7 148 149 153 154 158 162 167 169 173 175 176 233 473 475 476 478 479
Torsion form      139
Torsion-free connection      286
Torus      9
Total space      70 234 426
Totally real submanifolds      65 114
Totally symmetric spinor field      249 252 406
Totally-null two-planes      429
Totally-null two-surface      434
Transformation group      36 58
Transition function      8 10 18 76 78 83 86—91 111 112 121 122 124 195 235 307 324 361 375 386 404 451 454 459 462 472
Transition matrix      82 123 375 377- 386 387 391 394 399 403 408—409 410
Transition relation      391 452 455
Transitive group action      11 39
Translation      47 258
Trautman, A.      278
Treves, F.      359
Triangulation      52
Trivial bundle      91 197 204 272 308
Trivial line bundle      91 329 397 412
Trivial vector bundle      72 406
Trivializations      75 89
Tube domains      54
Twistor construction      296 297 371 409 423
Twistor correspondence      29 40 303
Twistor description      372 422 434 436 448
Twistor equation      455
Twistor flag manifolds      482
Twistor function      353 424 452 454 456
Twistor geometry      1 2 7 19 21 301 310 360 460
Twistor manifold      19 24 40 41 46 51 171
Twistor Newsletter      448
Twistor program      1 2
Twistor solution      428
Twistor space      2 19 21 29 39 40 51—53 64 130 270 277 279 293 301 350 371 373 378 379 382 391 398 422 423 433 435 436- 444—451 455 456 457 459 481 482
Twistor-geometric space      3 39
Two-component spinor      251 259
Two-component spinor bundles      126
Two-component spinor notation      241
Two-dimensional distribution      435
Two-dimensional surfaces      163
Two-form      244 290 292
Uhlenbeck, K.K.      272 278
Universal bundle      80 87 90 91 308 316 482
Universal line bundle      87 440
Unprimed indices      247 347 453
Unprimed spin-bundle      444
Unprimed spin-space      246 442
Unprimed spinor      442 450
Upper half-plane      55 62 356 358
Vacuum equations      448
Vacuum metrics      286 433
Vacuum solutions      454 456
Vacuum space times      451
Van der Waerden, B.L.      125
Van Moerbeke, P.      432
Variational Principle      241 253
Vector bundle      2 68—71 74 75 78 81—84 87 88 89 90 91 103 110 115 121 136—140 146 167 170 171 174 197 198 208 265 268 272 309 310 313 316 324 325 329 331 340 344 360 371 373 374 376 379 381 382 386 387 388 391 397 398 405 410 412 415 417 443 459 462 464 466 468
Vector bundle epimorphism      75
Vector bundle monomorphism      75
1 2 3 4 5
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