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Glimm J., Jaffe A. — Quantum Physics: A Functional Integral Point of View
Glimm J., Jaffe A. — Quantum Physics: A Functional Integral Point of View

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Название: Quantum Physics: A Functional Integral Point of View

Авторы: Glimm J., Jaffe A.

Аннотация:

This first Glimm-Jaffe edition as well as the extended second edition are the only textbook treatments of the Osterwalder-Schrader axioms and reconstruction theorem. The mathematically more tractable and usually convergent Euclidean theory is obtained by Wick rotating the time coordinate axis by 90 degrees (i goes to -1) in the Feynman Path Integral so that quantities (Green function integrals) arising from its expansion become exponentially damped and convergent rather than oscillatory. Under what conditions can we get the Feynman amplitudes in Minkowskian spacetime from these Euclidean quantities. This of course is the Osterwalder-Schrader theory. A thorough grounding in functional analysis and distribution theory at the level of the Reed-Simon texts(mostly volumes 1 and 2)is needed to understand the proofs. This material has lately found application in loop quantum gravity. For this alone either edition is worth having.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2

Год издания: 1987

Количество страниц: 558

Добавлена в каталог: 08.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Activity estimate      405
Analyticity      68ff 90 239 240 302 304 365ff 389 390
angular momentum      8 10 25 26 31 308 309 310 315
Anharmonic oscillator      12 18 111ff 119 120
Annihilation operator      13 116 180
Anomalous dimension      78
Anomalous magnetic moment      27 308 312ff
Asymptotic completeness      23 274 275
Asymptotic field      100 273ff 281ff
asymptotic freedom      438 459
Asymptotic state      276ff
atom      7 20
Axioms      89ff
Axioms, Bethe — Salpeter      301ff
Axioms, Euclidean      89ff 296
Axioms, Haag — Kastler      97 99ff 379
Axioms, Minkowski      97ff
Axioms, Osterwalder — Schrader      90 159ff 179 225 236ff 250ff 256 265 316ff 353 379ff 393ff 461
Axioms, verification of      250ff 255ff 265ff 316ff 320ff 393ff
Axioms, Wightman      97 256
Bessel's inequality      123
Bethe — Salpeter      188 275 300ff
Bilinear forms      129ff
Bochner theorem      148ff
Bogoliubov transformation      117
Boltzmann's constant      33
Borel summability      119 350 461ff
Bose — Einstein      117
Boson      11 32 92 116 117 160 215 463 464
Bound state      11 22 23 24 115 216 273ff 277 300 302 303 340 341 342 356
boundary conditions      37 150ff 177ff 189 194 199 219 235 242 464 465 471 see "Neumann"
Boundary conditions, monotonicity in      123 165 166ff 169ff 177 179 230 231ff 249ff 251 261
Boundary conditions, periodic      163ff 179ff
Boundary conditions, weak coupling      254 348
Brownian motion      43ff
Calculus on function space      202ff
Canonical      see "Ensemble"
Canonical exponent      160 349 350
Canonical quantization      111ff 296 344
Canonical, commutation relations      10 25 107 108 111 112 113 115
Canonical, coordinates      6 20 21
Casimir operator      26
Cayley's theorem      406
Channel      277
Channel, irreducible      301
Charge      20 see
Charge, density      307
Classical      6 86 see
Classical approximation      43 76
Classical critical point      78
Classical description      77
Classical differential equation      117 408
Classical exponent      349ff
Classical field      107 114
Classical force laws      28 311
Classical limit      3
Classical statistical mechanics      4 22ff
Classical trajectory      31
Cluster      23 24 68 273
Cluster, decomposition      276 277
Cluster, expansion      37ff 81 86 168 254 348 356ff 398ff 413 461 463 464 466
Cluster, property      283 286ff 359 365ff 394ff
Commutation relations      10 25 107 108 110 112 113 115
Conditioning      69 206 232 263
Configuration      82 83 84 86
Configuration, classical field      114 321
Configuration, space      114
Connected functions      286
Contraction semigroup      145
Cooperative phenomena      36 108 116
Correlation inequalities      56ff 78 81 119 200 220 225 229 417 427ff
Correlation inequalities for $P(\phi)_{2}$ fields      229ff 339 461
Coulomb      87
Coulomb force      28
Coulomb gas      465ff 469
Coulomb interactions      86 468
Coulomb potential      7 11 20 22 23
Coupling constant      43 119 215 216 218 342 411 see
Covariance operators      159ff see "Gaussian" "Boundary "Neumann"
Covariance operators in Gaussian integral, change of      208 210
Covariance operators, free      161ff
Covariance operators, lattice      219ff
Covariance operators, periodic      163ff
Creation operators      13 116 180
critical exponent      78 87 119 343 349ff 354
Critical point      30 56 73 77 78 80 118 119 160 320 339ff 345 348 353 356
Critical surface      30
Critical temperature      78 86
Cylinder, function      93 208 209 245 246
Cylinder, set      46 139ff
Defect index      127
density      28 32 35 37
Diagram      see "Feynman" "Mayer"
Diagram, charge      see "Vertex"
Diagram, mass      217 218
Diagram, skeleton      217
Diagram, vacuum      187
Dipole      86 87 331 469
Dirac equation      22 27 115 308ff
Dirac field      115 117
Dirac particle      312
Dirac sea      118
Dirichlet boundary conditions      37 160 161 165ff 168ff 177ff 219ff 230ff 234ff 243ff 249 264 324 339 see "Conditioning"
Dirichlet covariance      167ff 173ff 247 248
Dirichlet data      168 244 246ff
Dirichlet difference Laplacian      220
Dirichlet limit      209
Dirichlet monotonicity      230 231ff
distribution      53 75 89 90
Droplet model      81ff
Duplicate variable      57 59 60 64 65 67 72 366
Dyson equation      297ff
Electromagnetism      11 20 306ff
Energy      7 8 30 31 32 34 39 94ff
Energy-entropy bounds      405 421
Ensemble      30ff
Ensemble, Canonical      32ff
Ensemble, Grand Canonical      34ff 37ff 465ff 468ff
Ensemble, microcanonical      31ff
entropy      32 34 77 84 322
Entropy, estimate      405
Equation of motion      219ff see
Equilibrium      37
Equilibrium state      28ff 31ff 60
Ergodic      31 74 86 90 92 96 393ff
Essential self-adjointness      126 127
Euclidean      see "Axiom" "Field" "Functional
Euclidean propagator      see "Covariance operators"
Existence of quantum fields      157 250ff 271 359ff
Fermi field      160 462 463
Fermi — Dirac      115 117
Fermion      11 32 115ff 463 464
Ferromagnetic interaction      57ff 59 60 66 69 71 72 200ff 220 330
Feynman      43 44
Feynman — Kac formula      13 43ff 47ff 52ff 89 93 112 114 115 142 144 172 241 244 246 382ff 462 463
Feynman, graph, diagram      138 158 180ff 186 187 189 213 214 217 299 313
Field, Euclidean      89ff
Field, Minkowski      97ff
Field, strength renormalization      436
Field, theory      89ff
Fine structure      308 314 315
Fine structure constant      24 219 313
FKG (Fortuin — Kastelyn — Ginibre) inequality      64ff 229 317 318 319
Fock, representation      107ff
Fock, space      106 108 115ff 243 273 274 275
Fock, vacuum      281
Free energy      33 34 65 66 68ff 230 231ff 254 273 407 412ff
Free field      100ff 106ff 111ff 159ff 273 274 282 283 287 295 343 365 see
Friedrichs extension      129 131
Fugacity      35 65
Functional      92ff 202ff
Functional derivative      202ff
Functional determinant      206ff 211ff see
Functional integral      47ff 52ff 89ff
Gauge field      120 410
Gauge fixing      440 441 452 453 455
Gauge theory      87 409 410 437ff
Gaussian      see "Covariance operators" "Free "Integration
Gaussian critical point      119
Gaussian field      105
Gaussian functional      100 205 234
Gaussian functional integral of measure      49 90 100ff 106ff 111ff 180ff 183ff 186 188ff 205ff 208 209 211 226ff 235 243ff 253 357 360 366 460 466
Gaussian inequalities      428 432
Gaussian measure, translation of a      207
Gaussian measures      136ff
Gaussian process      119 226
Generating functional      53 55 90 101 102 104 105
Gibbs      31 34 356 357
Graph convergence      169
Green's function      159 161 255 332 333 342 see "Covariance "Dirichlet" "Neumann"
Griffiths inequalities      56 59 64 72 229 340 346 349 352 417
Ground state      see "State" "Phase"
Ground state, classical      75ff 85
Ground state, nonuniqueness of      73ff 78ff 81ff 320ff 393ff 422ff see
Ground state, quantum      11 13 19 25 51 85 93 95 113 115 310 see
Ground state, uniqueness of      50ff 74ff 86 97 340ff 356 359 393ff see
Haag — Kastler axioms      97 99 264 265 286 379 393 464
Haag — Ruelle scattering      274 275 286ff
Hamilton's equations      4ff
Hamiltonian      4 12ff 57ff 110ff
harmonic oscillator      12ff 106 111 112 119 189 244 246
Heat bath      32 33
Heat equation      44 288 see
Heat kernel      423
Heisenberg ferromagnet      37
Heisenberg model      235 330 331
Heisenberg picture      6 8 9 10
Helium atom      23
Hermite expansion      108
Hermite function      12 14 17
Hermite polynomials      14 15 106 109 180 189 204 206
Hermite recursion relation      185
Hierarchical model      79
Higgs      317 330
Higgs model      439 444
Hilbert space      122ff
Hoelder continuity      142 143
Hohenberg — Mermin — Wagner theorem      331
Hydrogen atom      11 20 23 24ff 314 315
Hydrogen atom, hyperfine structure      314 315
Ideal gas      29 35 37 77
Image charges      164 165
Index theorem      437
Infinite volume limit      56 59ff 229ff 249ff 255ff 337ff 463
Infra-red behavior      451ff
Instanton      37 470 471
Integration by parts      106ff 207ff 255 256ff 423 424
Ising limit      68 70 355
Ising model      36ff 59 66 69 70 73ff 81ff 119 235 320 341 349 351 412 416 470
Ising phase transition      73ff 81ff
Kirkwood — Salsburg equations      360ff 364
Klein — Gordon equation      115 283ff
Kosterlitz — Thouless transition      86ff
Lagrangian      44 215
Lamb shift      27 315ff
Lattice, approximation      118 209 219ff 225ff 442ff 446ff 454ff
Lattice, approximation, convergence of      209 222 227ff
Lattice, covariance operators      179 219ff
Lattice, fields      36ff 60 68ff 79 96 118 234ff
Lattice, Laplace operators      36 219ff
Lebowitz inequality      22 61 230 348 349 431
Lee — Yang theorem      56ff 65ff 81 229 230 336 339
Legendre transformation      34 36 44 188
Lehmann spectral formula      102 298 342 350
Lehmann — Symanzik — Zimmerman      275 295
Lennard — Jones potential      23 28
Lie product theorem      144ff
Linked cluster expansion      403
Liouville's theorem      5 31
Local stopping times      421ff
Locality      98 99 392ff
Lorentz covariance      92 98 100 309 389ff
Lorentz group      98 115 116 280 281
Magnetic dipole force      28
Magnetic field      65 310
Magnetic moment of electron      326ff
magnetization      80 81 306 319 336 340
Mass      20
Mass, center of      20 22 24 276 277 306
Mass, gap      287ff 359ff
Mass, operator      303 345
Mass, reduced      21
Mass, shift      206ff 211ff 216ff
Mass, skeleton      218
Mass, spectrum      274ff 300ff 356ff 461
Mayer graphs      40 357
Mayer series      38 41 76
mean field      70 75 79 85 86ff 330 349 356 465ff 467 469 470
Mehler's formula      19 48 244 246
Mermin — Wagner theorem      86 87 331
Microcanonical      see "Ensemble"
Minkowski      see "Axioms field"
Minlos' theorem      53 54 148ff
Moebius' theorem      286
Momentum cutoff      188 191 259 460ff see
Momentum scale      448
Monotonicity      see "Boundary conditions" "Conditioning" "Dirichlet" "Neumann"
Multiple reflection      see "Reflection"
Neumann      see "Boundary conditions" "Conditioning"
Neumann boundary conditions      159ff 164 177 178 230ff 253
Neumann covariance      164ff 327
Neumann limit      209
Neumann monotonicity      231ff
Neumann series      128
Non-Gaussian path space measures      52ff 193ff 248ff
Noninteraction theorem      433ff
Nuclear space      132ff
Observable      3ff 8 31 98 99 148 394
One particle irreducible      217
Operator, bounded      122
Operator, unbounded      122
Order parameter      80
Ornstein — Uhlenbeck      49 137
Osterwalder — Schrader      90 159ff 179 225 358 see "Reflection
Parallel transport      87 443ff 449
Particle, interpretation      273ff 280ff 286ff 300ff
Particle, reservoir      35
Partition function      33 57 66 68 69 81 212 231 243 263 298 327 360 367 370 465 466 468
Path      44 45 47
Path, space      48ff 52 93 157 168 182 239 462 see
Path, splitting      429ff
Pauli exclusion principle      11 23 28 151
Pauli matrices      312
Peierls' argument      82ff 321ff
Peierls' expansion      416
Perron — Frobenius theorem      51
Perturbation theory      43 186ff 255 296 297ff 313 461
Phase      73ff 79ff 81 82 99 316 317
Phase transition      30 38 56 65 66 70 72ff 73ff 99 119 199 316ff 330 333 339 348 378 461ff 469 470 471
Phase transition with no change in symmetry group      79 86 465
Phase transition with symmetry breaking      79ff 81ff 320ff 333ff
Phase transition, first order      81 317
Phase transition, higher order      320
Phase transition, proof of existence      81ff 320ff 333ff
Phase, boundary      82ff 321ff 400 416ff 464
Phase, cell localization      437ff 447ff
Phase, diagram      70 465
Phase, disordered      87
Phase, mixed      73ff
Phase, multiple      81ff 320ff 335 461 464ff
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