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Henneaux M., Teitelboim C. — Quantization of Gauge Systems
Henneaux M., Teitelboim C. — Quantization of Gauge Systems

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Название: Quantization of Gauge Systems

Авторы: Henneaux M., Teitelboim C.

Аннотация:

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied, and its equivalence with canonical methods is derived. The examples of electro-magnetism and Abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.


Язык: en

Рубрика: Физика/Квантовая теория поля/Теория калибровочных полей/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 540

Добавлена в каталог: 10.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Z_2$-grading      167 481
$\delta$-covering of phase space      198 228
Abelian constraints      196 285
Abelianization of constraints      113—117 324
Abelianization of gauge transformations      421 425
Acyclicity      172 195
Algebra of superfunctions      147 168
anomalies      279 290 301
Anti-BRST generator      251
Antibracket (definition)      367 416—417
Anticommutation rules — anticommutator      135 146 158 274 297 357 493 see
Anticommuting c-numbers      136
Antighost number      188 214—215 366 413
Antighosts      242 322 465
Antihermiticity      146
Associative algebra (definition)      166
Augmentation map      204
Automorphism      185
Auxiliary fields      42 43 97 247 426 427 447
B-field      247
Berezin integral      356 485
body      138 150
Boundary conditions — boundary terms      158—160 357 386
Boundary operator      171
BRST cohomology, classical      228 234—236 457—459 470
BRST cohomology, quantum      300—311 315 319—322 462—465
BRST differential      183
BRST observable      235 297
BRST symmetry      166 181 239 246 269
BRST-ghost number algebra      308
BRST-invariant extensions and constraints      236 301
BRST-invariant extensions definition      235
BRST-invariant Hamiltonian      238-239
Canonical Hamiltonian      9
Canonical phase transformations      431
Causal propagator      400
Chern — Simons theory      97
Chiral bosons      425
Chronological product (= time-ordered product)      339
Clifford algebra      275 319 493—500
Closed algebra (of gauge transformations)      72 79
Closed element      171
Co-exact states      328
Co-isotropic surfaces      53
Coboundary operator      171
Cocycle      see “Cycle”
Cohomologically trivial pairs      242 421
Cohomology      171
Cohomology of d modulo $\delta$      173 192
Commutator      see “Graded commutator”
Completeness of reducibility functions      209
Component along unity      137 138
Composition formula/rule      363 396
Consistency algorithm      37 83
Consistency conditions      12
Constraints first-class (definition)      16 17
Constraints irreducible      14
Constraints primary      5 83
Constraints reducible      14 25 80 208—213
Constraints second-class      20 29 31 55 157 203
Constraints secondary      12 83;
Contracting homotopy      172 176 268 458
Convolution      348
Counting operator      170 176 465
Covariant phase space      408
CYCLE      172
Darboux theorem      64 151 153
Decomposition of derivations of exterior algebra      186
Decomposition of the identity      334 335 350—351
Degree of freedom count      29 89
Delta function      491
Density of weight $\frac12$      293 331
Derivations      169
Differential      171
Differential complex      171 175
Differential modulo $\delta$      173 177 223
Dimensional regularization      438
Dirac bracket      23 56 273—275 381
Dirac conjecture      18 38 83
Dirac quantization      277—286
Dirac — Fock quantization      286—291 389
Doublet      308
Duality formula for operator cohomology      305—306
Duality formula for state cohomology      309
Effective action      394 435
Eilenberg — Cartan formula      119
Equations-of-motion gauge symmetries      70 95
Euler — Lagrange equations      4
Even component      139
Exact element      171
Exact sequence      204
Extended action      21 75 448
Extended Hamiltonian      20 90 448
Extended phase space      189—192 222 240 241
Exterior derivative      118 169 483
Exterior product      118 168 483
Extra ghost      247
Factor-ordering problem      196 273 278 297
Factorization of BRST-exact states      300—301
Factorization of null states      24
Faddeev — Popov action      244—246
Faddeev — Popov determinant      462 478
Faddeev — Popov measure      165
Feynman gauge      461 462
First-class constraints      see “Constraints”
First-class functions      15
Fock representation      288 298 313—316 498
Fourier components      464
Fourier transformation      363
Fractionalization of ghost number      299
Fradkin representation of integration measure      375
Fradkin — Vilkovisky theorem      390 398
Free algebra      167
Frolicher and Nijenhuis classification      185
Functional derivatives      66 253 254
Gauge conditions canonical      27 34 62 276 282 387
Gauge conditions derivative      91—92 101 241 245 247
Gauge conditions multiplier      93 239 401-402
Gauge conditions redundant      94 473
Gauge group      69
Gauge orbits      28 53 74 117 162
Gauge transformations and reparametrization invariance      107—109
Gauge transformations of extended action      75—82
Gauge transformations of Lagrangian action      82—91
Gauge transformations, as canonical transformations      78
Gauge transformations, as transformations not changing the physical state      16
Gauge-fixed action      239 269 432
Gauge-fixed BRST cohomology      444—445
Gauge-fixed BRST symmetry      443
Gauge-fixed Hamiltonian      239 243
Gauge-fixing fermion      239 243—244 389 432 443 449
Gauge-invariant extensions      34
Gauss law      456
Gaussian average      461 475
Gaussian integral      343 491
Generally covariant systems      19 102—109 280 399—400
Generating function      123 126 373 379
Generating sets (of gauge transformations) definition      71
Generating sets (of gauge transformations) irreducible      73
Generating sets (of gauge transformations) reducible      73
Generating sets (of gauge transformations) relation between different generating sets      74
Generators (of algebra)      167
Geometric ingredients of BRST theory      181—184
Ghost momenta      189
Ghost number      191 222 239 297 367 416
Ghost number zero states      309 322
Ghost of ghost      206 218 222 228 415
Ghost-of-ghost momenta      214—215 228
Global symmetries      82 94 99 see
Graded commutator      169 274
Graded differential algebra      171
Graded Lie algebra      169 378
Grading      169
Grassmann algebra (definition)      136
Grassmann parity      139 167 481 498 500
Green functions      341
Gribov obstruction      28 62 198 276
Hamilton principal function      124 129—130 247—249 396
Hamilton — Jacobi theory complete integral      124
Hamilton — Jacobi theory equation      124 126
Hamilton — Jacobi theory incomplete integral      124 127
Hamiltonian vector fields      52
Harmonic states      328
Heisenberg algebra      330 349
Heisenberg operators      334 338
Heisenberg picture      338 340
Hermite polynomials      353
Higher-order Lagrangians      47
Hodge decomposition theorem      328
Holomorphic quantization of second-class constraints      295
Holomorphic representation for bosons      346—349
Holomorphic representation for fermions      355—356 494 496
Holomorphic representation for indefinite metric systems      352—354 389
Homological algebra      166
Homological perturbation theory      177—181 187 220 223 410
Homology (definition)      172
Homology of $\delta$ modulo $\partial_kj^k$      263—269
Homotopy      see “Contracting homotopy”
Ideal      33 34 170 171 188
Im D      171
Imaginary time      338 352 355
Indefinite metric      287 349—355 356
Indefinite scalar product      326
Induced two-form      51
Infinite formal sums      181
Inner contraction derivation      186
Integrability conditions      279
Internal gauge symmetries      128 279 398
Involution      140 167
Irreducible constraints      see “Constraints”
Jacobi identity      24 50 147 169 270 367 483
Jordan Basis      302—305
Jordan blocks      303 304
Jordan canonical form      see “Jordan basis”
Ker D(definition)      171
Kernel (of an operator)      283 326 332 348 351 354 355 363
Kernel of the evolution operator      334 348 351 363
Koszul — Tate differential      189 213—216 263 364—366
Koszul — Tate resolution      183 187—189 216 412—414
Kunneth formula      250
Lagrange multipliers      11 13 242 310 322
Lagrangian submanifold      431
Landau gauge      461
Large-gauge transformations      31 278
Lefschetz trace formula      304 330
Left derivatives      138 151
Legendre transformation      9 10 343 394 435
Leibniz rule      169
Lie bracket      53 118 370 483
Liouville measure      336 356 381 438 492
Local commutativity      259
Local completeness      260
Local density      257
Local functional      254 432
Local gauge theory      259
Local measure      343
Local operator      185
Local p-forms      258 269
Local total divergence      256 257
Longitudinal algebra      168 189
Longitudinal cohomology      120
Longitudinal derivative      117 163 183 216—218 414
Longitudinal p-forms      117 168 189
Longitudinal vector fields      117
Lorentz gauge condition (for abelian two-form)      94 473
Main theorem of homological perturbation theory      177—181 192 214 411
Manifestly covariant gauges      241
Midpoint times      336
Mixed representation      334
Model (for differential complex)      217 221
Multi-ghost vertices      239 246 432
Multiplication rule for symbols      358 see
Negative norm states      149 287 290 297 310—311 350 353
Nijenhuis tensor      186
Nilpotency — nilpotent operators      171 181 184 297 418
Noether charge      94 95 246
Noether current      95
Noether identities      68 71
Noncanonical coordinates      151
Nonintegrated density      254
Nonlinear gauges      246
Nonminimal solution/sector      241—242 420—421 450 466 471—472 475—477
Nontrivial cycle      213—215
Normal symbol      347 354
Null oscillators      314 497
Null states      289
Null surfaces (of two-form induced on constraint surface)      53
Observables      33 54 108 182 228 235 309 386 409 416
Occupation number operator      314 353 465
Odd component      139
Odd constant      147
Odd-dimensional phase space      157—160
Open algebra      72 79
Operator equations      274
Operator insertions      338 349
Order of reducibility      211
p-forms      482
p-q symbol      335 339 351—352
p-vector fields      370 429
Parametrization      104
Parametrized systems      103—105 132 249 280 291 385—388
Parity automorphism      185
Partition function      338 355
Partition of unity      41 201 229 286
Path integral measure      344 345 432 436
Pauli matrices      158 361
Peierls bracket      411 427
Perturbative argument      268 271
Photons (temporal, longitudinal, transverse)      465
Physical scalar product      281 325
Physical states, physical state condition      278 283 289 299 309
Poisson algebra      235
Poisson bracket      12
Polynomial, polynomial algebra      167 175
Primary constraints      see “Constraints”
Principal fiber bundle      62
Projected kernel      284 323—326 364 395
Projection operator      328
Propagating gauges      244
Proper solution      418 424
Proper time      400
Pure ghost number      190 218 415
Pyramid      475
q-p symbol      337
Quadratic algebra      203
Quantum averages      338—340 365 392 433
Quantum BRST symmetry      369 433
Quantum gauge condition      290
Quartet      308 315 465
Quartet mechanism      314—315 471
Quotient algebra      33 171 188
Rank      197 269
Reduced configuration space      292
Reduced kernel      285
Reduced phase space      54 60 108 409 427
Reduced phase space quantization operator method      275—277
Reduced phase space quantization path integral      383—388
Reducibility equations      81 210
Reducibility functions      207—213
Reducible constraints      see “Constraints”
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