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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
Dodziuk, J.      275
Dolbeault cohomology classes      192
Dolbeault cohomology groups      113 185 361 362
Dolbeault complex      107 112 171 361
Dolbeault resolution      233 326
Dolbeault's theorem      185 233 322 326 342 363
Domains of holomorphy      193 194
Donaldson, S.K..      278 322 432
Double fibration      21 23 24 44 302 303 382 460 464 466 481—483
Double-fibration picture      351 372 444 447
Drell, S.D.      253
Drinfeld, V.G.      415 417
Dual bundle      75 91
Dual module      118 119
Dual projective twistor space      24
Dual twistor space      353 448
Dual twistors      353 371
Duality pairing      27 119 120 461
E-valued differential forms      134 146 168 184
Eastwood, M.G.      310 321 343 348 366 393 466 468 470
Edge of the wedge theorem      368
Eguchi, T.      294 295 297
Ehrenpreis, L.      366 367 370
Ehrlich, P.E.      122
Einstein convention      117
Einstein equations      459
Einstein metric      286 295 433
Einstein space      440
Einstein summation convention      53 394
Einstein — Weyl spaces      458
Einstein's vacuum equations      286 448
Einstein, A.      1 45 115 263 286 294 295 457 472
Electric charge      422
electric field      244 279 422
electromagnetic field      242 244 245
Electromagnetic forces      285
Elementary mapping      328
Elementary open set      374 391
Elementary particles      472
Elementary plane      372
Elementary state      353
Elliptic curve construction      414
Elliptic differential equations      113
Elliptic differential operator      227
Elliptic integral      425 430
Ellis, G.F.R.      253 286
Energy      281
Energy functional      281
Energy-momentum tensor      258
Euclidean coordinates      405
Euclidean four-space      46 270 371 423
Euclidean space      7 9 45 148 244 271 387
Euler characteristic      123 148 198 204
Euler homogeneity operator      353
Euler number      37 98
Euler — Lagrange equations      253 254 255 266—268 280
Exact form      94 114
Exact sequence      171 172 206 228
Exponential mapping      38 398
Exponential sequence      194 196
Extension theory      462
Exterior algebra      26 79 161
Exterior derivative      93 94 104 145 165 169 243 287 312
Exterior differentiation      132 134 221 302 310 335
Fairlie, D.B.      276
Ferbcr, A.      481
Fermionic fields      473
Feynman path integral      270
Fiber bundle      2 15 68 90 235 264
Fiber coordinates      102
Fibers      69
Field equation      148 253 257 268 362 263 265 309 347 348 382 451 459 484
Field theory      260 261 286 472
Filtered differential module      234
Fine resolution      328
Fine sheaf      182 183 184 195 197 232 233
Finite action      271 272 277
Finite energy      281 423
Finite-action critical point      274
Finite-action self-dual fields      274
Finite-action Yang — Mills solution      272
Finite-dimensional representation      84 85
First filtration      221 231
Flabby sheaf      355 370
Flag manifold      3 9 19 25 42 160 449 456 457 480
Flat connection      135 204 406
Flat space-time      290 433 434 444 454
Flat twistor space      434 444 448 449 454
Flume, R.      275
Formal extensions      462
Formal neighborhood      459—462 466 476
Formal power series      462 475
Four-current density      243 269 279
Four-dimensional Riemannian manifolds      278 294
Four-sphere      65 295
Fourier transform      1
Frame bundle      212 213 215
Free module      475
Freund, P.G.O.      295
Frobenius' Theorem      35 139 142 434
Frohlicher spectral sequence      238
Frohlicher, A.      228
Fubini — Study metric      147 295 457
Fulton, W.      414
Functional integral      270 271
Fundamental group      64
Fundamental representation      259 264 265 268 421
G-bundle      89 121 139 140 143 144 213 235
Ganoulis, N.      284
Gauge field      264 265 266 267 269 271—273 277 280 292 373 374 378 380 381 386 387 390 394 395 397 424 429 444 459
Gauge freedom      276 347 348 401
Gauge group      264 267 269 272 273 275 276 279 280 282 284 372 373 382 386 387 389 399 410 421 422
Gauge invariance      255 256 263 272 423
Gauge potential      264 266 269 272 292 372 373 375 377 378 381 387 402 404 408 412 413 423 430
Gauge theory      3 263—265 269—271 289 292 372
Gauge transformation      256 265 269 272 277 281 392 404 423
Gauss — Bonnet formula      204
Gauss' theorem      156
General linear group      36
General relativity      47 115 122 263 286
Genus      93 149
Germs      72
Gibbons, G.W.      294 296
Gilkey, P.B.      294 297
Gitler, S.      473
Glimm, J.      253 285
Global section      80 168 175 181 229 230 326 411 465
Goddard, P.      421 279 284 424 426 432
Godement, R.      162 166 176 182 230 232
Googly graviton      448
Graded algebra      474
Graded Lie algebras      473
Graded modules      224
Graded sheaf      228
Grading      225
Grand unified theories      280 285
Grassmann algebra      210 474
Grassmann, H.      1 7
Grassmannian      19 80 87 218 308 481
Grassmannian manifold      3 7 9 10 11 163 480
Grauert, H.      382
Gravitational instantons      293 295
Green's function      353 421 446
Green's theorem      109 156
Green, P.      459 467 480
Greenberg, M.J.      152 159 162—164 236
Griffiths, P.A.      147 166 185 192 193 196 201 202 204 462—464
Grothendieck, A.      166 479
Ground state      281
Guillemin, V.W.      359
Gunning, R.C.      15 185 382
Guth, A.H.      276
Hamad, J.      473 481 483 484
Hamilton's Principle of Stationary Action      253
Hamiltonian      280
Hamiltonian systems      432
Hanson, R.O.      294 297
Harmonic differential forms      192 227
Harmonic function      277 278 432
Harper, J.R.      152 159 162—164 236
Harris, J.      147 166 185 192 193 196 201 202 204
Hartogs — Riemann Removable Singularity type theorem      368
Hartogs' phenomenon      193
Hartshorne, R.      166 176 410—413 479
Harvey, R.      209 212
HausdorfT manifold      435
Hawking, S.W.      253 286 294—296
Helgason, S.      36 37 39
Helicity      331 338
Henkin, G.M.      459 467—469
Hermitian form      19 39 42 43 64 130 268 416
Hermitian manifold      46
Hermitian metric      144 309
Hermitian operator      251
Hermitian structure      390
Higgs field      267 426
Higgs potential      280
Higher homotopy groups      164
Higher-dimensional space-times      397
Higher-dimensional twistor spaces      397
Hilbert space      19 263
Hilbert, D.      354 368
Hill, C.D.      363
Hirzebruch, F.      85 86 166 176 179 214
Hitchin, N.J.      275—278 297 309 389—391 393 395 397 413 415 425—431 442 445 446 449 457 458
Hodge decomposition      192 193 227 228
Hodge numbers      228
Hodge star-operator      243 273 292
Hodge theory      185 192 228
Holomorphic bundles      397 422
Holomorphic connection      293
Holomorphic coordinates      101 359
Holomorphic curve      429 438 442- 446 451 452 454 455 457
Holomorphic extension      358 463
Holomorphic function      8 15 79 85 108 109 158 168 174 175 183 184 189 293 306 340 345 349 355 356 358 359 368 372 383 384 387 394 399 435 454 455 461 476 477 479 480
Holomorphic line-bundle      85 86 195 196 382 383 429 441
Holomorphic mapping      8 10 18 44 476 477
Holomorphic metric      293
Holomorphic p-forms      108 109 168 171 184 351 441
Holomorphic rational curves      436 441
Holomorphic right-handed massless fields      331
Holomorphic section      79 87 304 374 377 379 386 390 427 428 438 439 446
Holomorphic structure      381 388 429
Holomorphic super vector bundle      484
Holomorphic tangent bundle      100 101 114 426 427 442
Holomorphic vector bundle      71 72 79 81 101 112 168 171 184 185 233 303 304 307 316 325 326 330 342 361 362 37' 372 374 375 377 382 386 389 390 394 398 410 423 428 459 460 462—464 466 480 483
Holomorphic vector field      100 426 427
Holomorphic Yang — Mills bundle      464- 467 469
Homogeneous coordinates      12 22 23 26 28—31 53 58 130 147 351 373 375 410 415 438 457 461
Homogeneous differential form      93 147
Homogeneous space      36 38 39 41 45 84 163
Homogeneous vector bundles      84 85
Homology class      192 159
Homology groups      150 151 153 156 157 159 161—163 165
Homology invariants      148
Homology theory      176
Homotopic curves      158
Homotopy equivalence      150 159 164
Homotopy groups      150 153 163 164 165
Homotopy invariants      148
Hopf bundle      278
Horizontal subspaces      143 144 389 445
Horizontal vectors      141 142
Hormander, L.      114 185 189 194 342 359 389
Horrocks, G.      372 415
Horvath, Z.      431
Huang, K.      285
Hughston, L.P.      397
Hulek, K.      415 417
Hurtubise, J.      422 432 473 481 483 484
Hydrogen atom      263
Hyper-Kaehler spaces      449
Hyperbolic differential equations      2 149 166 257 354
Hyperfunction data      362 363 366 369
Hyperfunction differential forms      359
Hyperfunction Dolbeault groups      361
Hyperfunction massless field      367
Hyperfunction Penrose transform      364
Hyperfunction solutions      301 302 354 360—362
Hyperfunction tangential Dolbeault groups      362
Hyperfunction-valued forms      360
Hyperfunctions      354 356
Hyperplane section      30 162
Hyperplane section bundle      86 125 184 191 192 195 196 203 303 304 308 310 325 341 349 403 411 436
Hyperplane section sheaf      302 316
Hypersurface twistors      433
Ideal sheaf      339 343 461 463 479
Induced connection      136 137
Inductive limit      173 174 178 219 223 238
Infinite series      358 370
Infinite-dimensional cohomology      191
Infinitesimal neighborhood      339 463 464
Inhomogeneous Cauchy — Riemann equation      187
Inhomogeneous Maxwell equations      467
Inhomogeneous Yang — Mills equations      467
Instanton bundle      410 411 413 415
Instanton connection      410 420
Instanton field      275
Instanton number      273
Instanton solutions      372
instantons      273
Integrability conditions of Frobenius      143
Integrable almost-complex structure      114 389
Integrable distribution      444
Integral cohomology      162 176
Integral cohomology group      160 199
Integral de Rham class      200
Integral formula      21 302 349 354 368
Integral geometry      3
Integral homology      162
Integral surface      444 447
Integral-geometric transform      3 149 302
Interior product      27
Invariant polynomial      199 200 201
Inverse correspondence      20 21 303
Inverse Penrose transform      470 471
inversion      60 260
Isenberg, J.      459 467
Isotropic flags      42 43
Isotropic submanifolds      482
Isotropy group      39
Jackiw, R.      276 278
Jacobian      430 432
Jacobian matrix      15 344
Jaffe, A.      253 275 279 281 285
Jones, P.E.      458
Jumping lines      413
K3 metrics      295
K3 space      295
Kac — Moody algebras      473
Kac, V.G.      473
Kahler manifold      146 147 185 192 227 228 295
Kahler potential      114
Kahler structure      449
Kashiwara, M.      367
Kawai, T.      367
Killing form      265 266 268
Killing spinor equation      455
Killing spinor field      456
Killing vector      448 456
1 2 3 4 5
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