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Bertlmann R.A. Ч Anomalies in Quantum Field Theory
Bertlmann R.A. Ч Anomalies in Quantum Field Theory



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Ќазвание: Anomalies in Quantum Field Theory

јвтор: Bertlmann R.A.

јннотаци€:

An anomaly is the failure of a classical symmetry to survive the process of quantization and regularization. The study of anomalies has played an important role in quantum field theory in the last 20 years, one which is described clearly and comprehensively in this book, the first textbook on the subject. The author approaches the subject through differential geometry, a method that has received much attention in recent years, and gives detailed derivations and calculations which will be invaluable to both students and researchers in theoretical and mathematical physics.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1996

 оличество страниц: 566

ƒобавлена в каталог: 26.11.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\phi^{4}$ theory      142Ч149
$\pi^{0}\rightarrow\gamma\gamma$ decay      233Ч238
't Hooft Ч Veltman integral formula      207 222
't Hooft Ч Veltman regularization      207Ч210 220Ч223
Action principle      492
Action, active coordinate transformations      470 472Ч474
Action, adjoint derivative      51Ч53 294
Adjoint map      94
Adjoint operator      412
Adjoint representation      94 161
Adler Ч bardeen theorem      205
Aharonov Ч Bohm effect      306Ч311
Aharonov Ч Bohm effect, fibre bundle description      309
Aharonov Ч Bohm effect, phase shift      308
Aharonov Ч Bohm effect, quantum mechanics      307
Anomalous divergence      188 214 219 253
Anomaly      176 188 193Ч195 212Ч214 296Ч297 338 353 354 365 366 378 410 426
Anomaly and phase      194Ч195 440
Anomaly cancellation      245Ч247
Anomaly for L-currents      190
Anomaly formula      341
Anomaly shift      517
Anomaly, 2-dimensional      214Ч227 260Ч261 276 283 286
Anomaly, ABJ      188 197Ч214
Anomaly, Bardeen      241 243 297 351 436 446
Anomaly, consistent      243 272 401
Anomaly, covariant      243 266 270 271 297 393Ч394 397Ч400 405
Anomaly, dispersion relations      216Ч220
Anomaly, IR behaviour      230Ч231
Anomaly, non-Abelian      241Ч244 265Ч272 297 338 379 382 435Ч436 445Ч446
Anomaly, nonlocal extensions      406Ч407
Anomaly, normalization      369
Anomaly, regularization independence      261Ч263
Anomaly, singlet      238Ч241 259 296 379 381 400 411
Anomaly, UV behaviour      231Ч232
Anti-BRS transformation      175
Antiderivation rule      43 333
Associated bundle      103
Atiyah Ч Singer index theorem      305 319 410Ч411 426Ч427 443 534 541
Atlas      31
Axial current      178
Axial current, non-Abelian      183
Axial gauge      169
Background field      371
Bardeen Ч Zumino counterterm      515
Bardeen Ч Zumino polynomial      392Ч393 396Ч400 404Ч405 519 541
Base space      95
beta function      388
Betti numbers      69Ч71
Bianchi identity      165 295 354 463 480
Bianchi identity, first      482
Boundary      11
Boundary operator      62
Bounded operator      412
BRS algebra      376 520Ч524
BRS algebra for nontrivial fibre bundles      528Ч529
BRS algebra, shifted      524Ч525
BRS operator      172Ч175 345 350 356 379 523
BRS operator, shifted      524
BRS operator, total      521
BRS transformation      172Ч175 345Ч346 357 358 366 521
Cartan structure equation      114Ч116 463 479
Cartan's exterior algebra      42
Cartan's homotopy formula      334
Cauchy's integral formula      217
Chain complex      62
Chain terms      352 354 369 537
Chain terms, solutions      382Ч383 386 389
Chains      61
Charts      31
Chern character      425
Chern number      305 319 327
Chern Ч Simons form      296 314 327Ч328 335Ч337 354 367 372 377 379 444 516 525 527
Chern Ч Simons form, gauge transformation      336Ч337
Chern Ч Simons form, variation      339 341
Chern Ч Simons term      240
Chern Ч Simons theory      379
Chiral transformations      181 250Ч251 256 267
Chiral transformations, Jacobian      280Ч286
Chirality split      268
Christoffel connection      460Ч461
Christoffel connection, transformation      469 471 474
Christoffel symbol      460
Closed set      10
Closure      10
Coboundary      67 364 378
Coboundary operator      363
Cochain      363
Cocycle      67 362 364 378
Cocycle condition      361 364
Coderivative      see "Adjoint derivative"
Cohomology      363Ч365 378Ч379
Cokernel      413
Commutation relations functional      391
Compactification      13 17
Compactness      12
Compatibility condition      112 117 304 317 442 443
Conformal group      456
Conformal transformation      456
Conformally flat manifolds      456Ч458
Connectedness      18
Connection      105Ч113 304 309 317
Connection 1-form      109Ч112 442 460
Connection, global      443
Conservation laws      177Ч185 228
Consistency conditions for gravitational anomalies      512Ч515 522 529
Consistent current      392
Consistent current, gauge transformation      392 396 402Ч403
Continuous map      13
Contractible space      329
Contravariant vector      459
Coordinate transformations      458Ч460 468Ч474
Coordinate transformations, infinitesimal      470Ч471
Coordinate transformations, matrix      469
Cosmological constant      493
Cotangent bundle      104
Cotangent space      39Ч40
Cotangent space, basis      39 373
Covariant anomaly condition      394
Covariant current      392Ч393 397 404
Covariant current, gauge transformation      393 404
Covariant derivative      113 162 163 181 343 376 461 467Ч468 479 496
Covariant vector      459
Covering      12
Current 1-form      296 395
Current 1-form on Sp $\mathcal{A}$      401
Current operator      210Ч214
Curvature      113Ч117 304 310 463Ч465 479 484
Curvature 2-form      114 443
Curvature, transformation      469 471 473
Cutkosky rule      225
CYCLE      63
d'Alembert operator      420
De Rham cohomology      67Ч73
de Rham cohomology, group      67
de Rham cohomology, inner product      70
de Rham complex      68
de Rham's theorem      69
Derivative in Sp $\mathcal{A}$      391
Descent equations      341 354 369 372 376 377 385 387 525Ч527 530
Determinant bundle      448Ч449
Determinant fermion      439
Determinant of a differential operator      137Ч139
Determinant of the Dirac operator      277Ч286
Determinant of the metric      453
Determinant of the Weyl operator      428
Determinant, gauge invariance      429Ч430 439
Determinant, phase      439Ч440
Determinant, regularized      277 280Ч286
Diffeomorphism group      469
Diffeomorphisms      13 532
Differential forms      40Ч58 84
Differential forms on Sp $\mathcal{A}$      348
Differential forms, anticommutator      56Ч58
Differential forms, closed      54
Differential forms, coclosed      54
Differential forms, coexact      54
Differential forms, commutator      56Ч58
Differential forms, exact      54
Differential forms, harmonic      54 71Ч72
Differential forms, inner product      51
Differential forms, integration of      45Ч46
Differential forms, trace      56
Differential map      73 89
Dilatation vector      475
Dirac equation      154 178 229
Dirac equation, energy spectrum      229
Dirac field, free      154 155
Dirac field, interacting      155Ч156
Dirac genus      534
Dirac monopole      297Ч306 380 426
Dirac monopole, fibre bundle description      303
Dirac monopole, field strength      302
Dirac monopole, gauge potentials      299 301 302
Dirac monopole, gauge transformation      300Ч302
Dirac monopole, magnetic charge quantization      301
Dirac monopole, winding number      305
Dirac operator      249 255 265 497
Dirac operator, construction on $S^{2}\times S^{2n}$      441Ч443
Dirac operator, eigenvalue equation      409
Dirac operator, spectrum      431
Dirac operator, zero modes      409
Dirac sea      227Ч233
Dispersion relations      216Ч220
Dual algebra *Lie G      358
Dual current form      296 395
Dual p-form      49
Duality      68
Einstein anomaly      509Ч510 533 536
Einstein anomaly, 2-dimensional      537
Einstein equation      492Ч493
Einstein equation, with matter      493
Einstein equation, without matter      492
Einstein ghost      521
Einstein invariance      504Ч505 519
Einstein tensor      493
Einstein transformations      474 504 518Ч519
Einstein transformations, generator      511
Einstein Ч Hilbert action      491
Electrodynamics      287
Electrodynamics, action      292
Electrodynamics, current conservation      292
Electrodynamics, field strength      178
Electrodynamics, field strength tensor      288
Electrodynamics, gauge potential      156Ч159 290
Electrodynamics, Lagrangian      177
Elliptic differential operators      417Ч420 422
Embedding      454
Energy-momentum tensor      493Ч495 508 519
Energy-momentum tensor, antisymmetric      509
Energy-momentum tensor, covariant      519
Energy-momentum tensor, covariant conservation      493 505
Energy-momentum tensor, symmetric      493 503 504
Energy-momentum tensor, traceless      507
Equivalence principle      458
Euclidean space      250
Euclidean space, 2-dimensional      261
Euler characteristic      69Ч71
Exponential map      90
Extended gauge group element      374
Exterior covariant derivative      113
Exterior derivative      42 373 443
Exterior derivative in Sp $\mathcal{A}$      348 360
Exterior derivative in Sp $\mathcal{M}$      518
Exterior derivative on $\mathcal{M}\times \mathcal{G}$      374
Face      59
Faddeev Ч Popov determinant      167
Faddeev Ч Popov ghosts      92 168Ч170 344 350 356 379
Faddeev Ч Popov operator, differential      345
Faddeev Ч Popov operator, integrated      345
Family index theorem      436
Fermionic action      497
Fermionic Lagrangian      500Ч502
Feynman gauge      159
Feynman parameter integral      206 221
Feynman propagator for fermions      154Ч155
Feynman propagator of the photon      158Ч159
Feynman propagator, scalar      137
Feynman's path integral      124Ч129
Feynman's path integral, formula      126
Feynman's path integral, Hamilton formalism      126Ч129
Fibre bundles      95Ч117 348
Fibre bundles, reconstruction      99Ч101
Fibres      95 304 316
Field strength      116Ч117
Flow      78Ч81 90 93 105
Flow, infinitesimal      79
Frame bundle      104
Fredholm alternative      415
Fredholm operators      413Ч414 420
Fredholm operators, direct sum      415
Fredholm operators, product      416
Fujikawa's method      255Ч259
Fujikawa's method, regularization      257Ч259 263 268 270 432Ч435
Fujikawa's uncertainty principle      263Ч265
Function of an operator      274
Functional derivative      132Ч135 347
Fundamental vector field      105 360
Fundamental vector field, commutator      401
Gamma function      278
Gauge condition      166
Gauge fixing      158 167 169
Gauge group      159Ч161
Gauge group space      347 374 447
Gauge operator      343Ч344 353 356 360
Gauge operator, commutation relations      343 353
Gauge operator, integrated      344
Gauge potential      110Ч113 162
Gauge transformations      112 161 270 374
Gauge transformations, axial      179 181
Gauge transformations, infinitesimal      164
Gauge transformations, left-handed      180 182
Gauge transformations, right-handed      180 182
Gauge transformations, vector      178 181
Gauge variation      344
Gauss theorem      467
Gaussian cut-off      257 434
Gaussian integration      137Ч139 259 435
Gaussian integration for Grassmann variables      151Ч154
Gell-Mann matrices      160
Generating functional      140 142 144 154 155 169 191Ч197 251 342
Graded algebra      173
Grassmann algebra      42 149Ч154
Grassmann differentiation      150
Grassmann integration      150 256 264 433
Grassmann measure      256 267
Gravitational anomaly formula      527 531
Gravitational anomaly, axial      542Ч543
Gravitational anomaly, covariant      518Ч520 540
Gravitational anomaly, normalization      536
Gravitational anomaly, total      522
Green functions      185Ч190
Green functions for interacting fields      144Ч147
Green functions, connected      147Ч149
Green functions, free      139Ч141
Gribov ambiguity      171Ч172
Group parameter space      372
harmonic oscillator      121
Heat equation      274Ч275
Heat kernel      274Ч276 423Ч425
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