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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
$\alpha$-plane      25 32 35 314 372 434
$\beta$-plane      25 32 35
$\mathbb Z_2$-graded ring      474 475
$\mathbb Z_2$-grading      474
$\mathcal H$-space      294
$\mathfrak g$-valued one-form      140 141 144 264 276
't Hooft solutions      420 421
't Hooft, G.      283
Abstract de Rham theorem      182 232 327 328
Abstract index notation      115 118 121 241 287 310 317
Abstract indices      121 129 242 247
Action principle      241 252 253
Acyclic differential sheaves      232 233
ADHM construction      372 410 421 422 430
ADHMN construction      431
Adjoint representation      89 264 265 267 280 423
Adler, M.      432
Affine coordinate system      57 59 190 320
Affine Euclidean space      66
Affine Minkowski space      22 66 301
Affine spaces      46
Affine super Minkowski space      482
Affine transformations      51 52
Ahlfors, L.V.      150
ALE metrics      457
ALE spaces      295 297
ALF spaces      295
Algebra      72 80
Algebraic curve      432
Algebraic geometry      2 23 84 166 410 473 476 478
Algebraic topology      2 149 150 153 157 166
Almost complex structure      14 121 124 388 389 445 446
Almost complex tensor      102 114
Ambitwistor space      24 433 459 460
Analytic pullback      304
Analytic space      478
Analytic subvariety      477 478
Ansatz solutions      278
Anti-self-dual conformal curvature      443 447 451
Anti-self-dual connection      389 406 422 466
Anti-self-dual curvature      373
Anti-self-dual Einstein metric      294 442 443 445 456 457
Anti-self-dual Einstein space      295 451
Anti-self-dual fields      274 302 371 372 386 398 410 444
Anti-self-dual gauge potential      394 420
Anti-self-dual instantons      275 295 410 413 414
Anti-self-dual Maxwell field      338 382 383 422 456
Anti-self-dual part      257 266 273 287 293 294 312
Anti-self-dual pp-wave      456
Anti-self-dual space-time      293 295 433 434 444—446 448 449 455
Anti-self-dual two-form      273 276 312 347 373
Anti-self-dual vacuum space      294 295 296 439 450
Anti-self-dual Weyl spinor      454
Anti-self-dual Weyl tensor      295
Anti-self-dual Yang — Mills equations      371 378
Anti-self-duality      373 396 397
Anti-self-duality equation      266 380 398 423 429
Anti-selfrdual gauge field      374 380 386 389 390 393 395—397 403 404 407 409 418 423 443
Antiholomorphic involution      387 412 428 445
Antipodal map      391
Associated graded module      224
Associated principal bundle      144
Associative algebra      136
Asymptotically Euclidean      294
Asymptotically flat space-times      294
Asymptotically locally Euclidean (ALE)      294 296 457
Asymptotically locally flat (ALF)      294
Athorne, C.      409 430
Atiyah — Drinfeld — Hitchin — Manin (ADHM) construction      372 410 421 422 430
Atiyah — Hitchin — Singer theorem      410
Atiyah — Singer index theorem      275
Atiyah, M.F.      86 209 275—277 353 371 389—391 404 410 413 415 417 421 422 445 446
Axial current      467
Axially-symmetric solution      424 425
Bagger      473
Bailey, T.N.      366 367 370 422
Barth — Horrocks monad construction      484
Barth, W.      415 417
Base space      70 195 197 276
Batchelor, M.      480
Bateman, H.      47 349
Beem, J.K.      122
Belavin, A.A.      276 278
Berezin, F.A.      460 473
Bernard, C.W.      276
Betti number      150 151 157 161 162 165 204 228 328
Betti, E.      148 150
Bianchi identity      137 201 266 269 283 287 292 454
Bicomplex module      220
Bigraded module      220
Bjorken, J.D.      253
Blanchard, A.      449
Bochner, S.      54 55 192
Bockstein mapping      181
Bogomolny equations      283 284 422 428 429 431 432
Bott, R.      209
Boundary value      301 355—359 363 364 367 368
Bounded holomorphic functions      172 174 175
Bourguignon, J.P.      274 275
Bowman, M.C.      431
Boyer, C.P.      294 473
Bredon, G.E.      166 176 182
Brown, L.      276
Brown, S.A.      431
Brownian motion      270
Bryant, R.L.      449
Buchdahl, N.P.      331 468
Bundle automorphism      269
Bundle mapping      70
Burzlaff, J.      409
Canonical connection      46
Canonical line bundle      124 309 442
Canonical resolution      229 230 234
Canonical Riemannian connection      274
Canonical transformation      452
Carlitz, R.      276
Cartan's Lemma      28
Cartan, E.      2 37 125
Cartan, H.      2 166
Cauchy integral formula      55 109 189 342
Cauchy theorem      158 351
Cauchy — Riemann equation      7 101 107 113 360
Cauchy — Riemann operator      107
Cauchy's integral formula      384
Cayley transform      62
Cech cohomology      178 230 326
Cech covering      153 302 326 359
Cech theory      176 182
Cell complex      62
Cell decomposition      153 263
CF'tHW ansatz      424
Characteristic class      3 123 148 197- 199 205 214 462
Cheng, T.P.      285
Chern class      199—203 205 217 218 280 283 399 411 415 417
Chern form      192 202 207
Chern number      273 278 280 399 410
Chern, S.S.      199 201—204 218 403
Chow's theorem      15 16
Christ, N.H.      276 418 421 422
Civilized neighborhood      435
Civilized regions      444
Civilized spaces      436 440
Clarke, C.J.S.      473
Classical field equations      263
Classical field theory      2 21
Clifford algebra      208 209 215
Clifford group      210
Clifford multiplication      209 251
Clifford relations      251
Closed differential form      94 114 147 161 192 200 202 243
Closed orbit      44 66
Coboundary      160 178
Coboundary operator      159 177
Cocycle      160 178 195
Coherent sheaves      342
Cohomology class      178 181 183 191 192 198 202 203 207 322 235 237—339 341 343 363 463
Cohomology group      95 113 151 153 159 161 163 165 178 182 196 197 213 222 224 229 325 327 332 339 341 361 362 366 383 394 396 418 447 452 459 463
Cohomology set      206
Cohomology theory      166 176 206 208
Combinatorial topology      152
Compact complex manifold      10 11 12 18 19 25 41 52 185 189 191
Compactified complexified Minkowski space      64 65 201 481
Compactified Minkowski space      215
Compactified space-time      413
Compactified super Minkowski space      482
Complementary bundle      308
Complete intersection      412
COMPLEX      95
Complex conjugation      246
Complex coordinates      163 297 457
Complex general linear group      36
Complex Grassmannian manifold      27 28
Complex Lie groups      41
Complex light cone      49
Complex line bundles      198 199
Complex manifold      8 9 10 15 16 18 19 44 51 81 85 96 100 103—106 112 113 114 146 148 168 171 173 176 183—185 208 225 233 309 339 342 349 359 360 369 387 388 426 433 436 446 476—480
Complex manifold structure      41 114
Complex Maxwell field      403
Complex null geodesies      433
Complex projective line      65 192 349 436 445
Complex projective space      7 9 163 210 227 295 416
Complex self-dual spaces      294
Complex space-time      293 294 433 434 444
Complex structure      102 114 216 389 427 433 444—446 476
Complex submanifold      8 9 15 16 18 28 44 339 349 434 436 461 476
Complex supermanifold      479
Complex vector bundle      71 88 124 125 127 132 199 201—203 310 388
Complexification      18 50 103 125
Complexified compactified Minkowski space      64 65 210 481
Complexified conformal group      381
Complexified Euclidean metric      402
Complexified flat space-time      297
Complexified Minkowski space      22 49 58 460
Complexified space-time      402 403 405
Complexified tangent bundle      103
Conformal compactification      46 52 61 301 354
Conformal curvature      435
Conformal curvature tensor      287
Conformal density      291 292
Conformal factor      290 439 450
Conformal group      47 58 260 261
Conformal invariance      30 241 258 261 272
Conformal mapping      258 259 260 272
Conformal metric      439 453 454
Conformal rescaling      61 259 261 263 267 271 286 288 289 436 454
Conformal structure      30 51 260 433 435 439 442 446
Conformal transformation      52 259 261 293 470
Conformal weight      261 262 291 292 308 309 310 334 361 436
Conformally invariant field equations      291
Conformally invariant operators      335 446
Conformally weighted scalar fields      334
Conformally weighted spinor bundles      302 313
Conformally weighted spinor fields      311 331
Connecting homomorphisms      181 213
Connection      111 118 132 145
Connection differential operator      134
Connection one-form      133 141 142 146 201 203 205 269
Conormal bundle      339 346
Conormal sheaf      228 235 236 343 344
Constant sheaf      169 184
Constraint equations      483
Continuous linear functional      354 358
Contour integral      322 349 350
Contour integral formula      349 428
Contraction operation      117 138
Convergent power series      72 109 475
Coordinate chart      8 10—12 14 15 17 19 22 53 54 62 65 66 74 76 81 97 100 163 189 315 343 350 376 378 383 391 394 399
Coordinate mapping      8 22 73
Coordinate representation      24 25
Coordinate system      48 76 82 123 248 456 478 481
Correspondence      21
Correspondence space      20 21 23 24
Corrigan — Fairlie — 't Hooft — Wilczek ansatz      423
Corrigan, E.F.      276 371 397 404 421 424 426 432
Cosmological constant      287
Cotangent bundles      79 96 297
Courant, R.      354 368
Covariant derivative operator      242 287 395 420
Covariant differentiation      118 121 138 139 145 209
Covariantly constant basis-spinors      447
Covariantly constant field      376
Covariantly constant frame      139 143
Covariantly constant sections      422
Covariantly constant two-form      407
Cross section      69
Curtis, W.D.      441 444 454
Curvature      35
Curvature form      139 142 143 204 269 373
Curvature tensor      287 292 293
Curved space-time      145 261 287 293 433 435
Curved twistor space      433 434 439 448 451 452
d'Alembertian      242 261 288
Daniel, M.      275
de Rham class      202
De Rham cohomology      161 199 226
de Rham cohomology class      201
de Rham cohomology groups      95 98 151 161 185 199 202 226
de Rham complex      96 108 110 169 170 228 312
de Rham resolution      232
de Rham sequence      313 348
de Rham theorem      176 185 199 232
de Rham, G.      107 161 359
de Roo, M.      422
De Witt, B.S.      473
Decreasing filtration      220
Deformation, infinitesimal      451 452
Derivation      72
Differential      218
Differential equation      21 342 347 361 431 444 483
Differential form      80 82 83 92 94- 103 104 no ;;; 115 137 138 140 160 161 165 172 192 200 202 205 228 232 305 307 308 338 339 359 439
Differential geometry      192 227
Differential operator      112 139 144 260 264 302 303 331 334 430 447
Differential sheaf      218 230—232 234 238 327 337
DifTerentiable bundle      388
DifTerentiable manifold      8 9 13 16 61 72 79 82 92 95 107 110 114 115 131 132 142 160 161 169 183 194 197 213 228 232 235 237 309 476
DifTerentiable manifold structure      74 476
DifTerentiable mapping      8 13—15 68 203 206 208 213 324
DifTerentiable sections      72 197
DifTerentiable supermanifold      480
DifTerentiable vector bundle      71 72 146 197 199 324 480
Dilation      60 260
Dimensional reduction      423 458
Dirac delta function      357
Dirac equation      241 250 252 254
Dirac field      254 255
Dirac Lagrangian      254 256
Dirac magnetic poles      279 422
Dirac measure      357
Dirac operator      209 469
Dirac poles      282 422
Dirac spin-space      255
Dirac spinor      241 251 252 268
Dirac spinor notation      251 252 254
Dirac, P.A.M.      1 125 279 459
Direct image      303 315—317 319 323 335 336
Direct image sheaves      318 333 382
Directional derivative      12 13 18 73 74
Distribution coefficients      359
Distributions      354
Divisor      85
1 2 3 4 5
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