Bratteli O., Robinson D.W. — Operator Algebras and Quantum Statistical Mechanics (vol. 2) :: Электронная библиотека попечительского совета мехмата МГУ

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Bratteli O., Robinson D.W. — Operator Algebras and Quantum Statistical Mechanics (vol. 2)

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Название: Operator Algebras and Quantum Statistical Mechanics (vol. 2)

Авторы: Bratteli O., Robinson D.W.

Аннотация:

For almost two decades this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMS-condition and stability, quantum spin systems and continuous systems.
Major changes in the new edition relate to Bose — Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Notes and remarks have been considerably augmented.

Язык:

Рубрика: Физика/Термодинамика, статистическая физика/Квантовые методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2002

Количество страниц: 517

Добавлена в каталог: 29.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

DuHamel two-point function      93 221 225
Duneau and Souillard      459
Dunford      155
Dye      305
Dynamical flow      159
Dynamical system      13 136 137
Dynamical system, C      136 137 139 142 310 76—106 204 212—214 235 422 423
Dynamical, W      136—142 310 77—81 114 123 144 150 158 165—170 178 212- 237
Dynamics      159 160 4 5 45—62 72 78 119 144 176 239 250 251 348 349 427
Dynamics, perturbed      97
Dyson      232
Dyson and Lenard      447
Dyson, Lieb and Simon      441
Effros      465
Einstein      442
Element, analytic (entire)      97—101 115 178 231 265—267 272 293 76—80 84 94 157 158 167 207—210 244—248 277 307 334 432 analytic”)
Element, even      121 162
Element, identity      see “Identity”
Element, invertible      25 38 213
Element, isometric      28
Element, normal      28
Element, odd      121 162
Element, positive      7 32 38 215 276 27 92 94 116 123
Element, quasi-analytic      311
Element, self-adjoint      28 103 147 212 213
Element, unitary      28 38 72 97 107 110 111 214 384 395 417 418 411 102 145 146 211—214
Elliott      152 306 309 311
Ensemble, Canonical      4 437
Ensemble, Grand Canonical      4 46 437
Ensemble, microcanonical      4
entropy      89 268—302 432—435
Entropy, conditional      268 274—284 295 432 434
Entropy, maximal conditional      275
Entropy, maximum      89 90 221 267 273 274 286—300 340 422 435 444
Entropy, mean      290 292 296 300—302 348 434
Entropy, per unit volume      270
Entropy, relative      267—270 275—280
Entropy, total      270 271
Envelope, lower      326 327
Envelope, upper      326—328 335 338
Equicontinuity      167 185
Equicontinuous, $\tau(X,F)$       168 174 204
Equivalence, physical      14
Equivalence, quasi      79—82 128 370 395 452
Equivalence, unitary      48 56 79 80 151 283 396 429 442 450 457
Ergodic theory      13 401 423 432 435 “Decomposition” “State”)
Ergodicity, central      395
Evans      225 226
Evans and Hanche — Olsen      222
Extension, canonical      52 58 60
Extension, state      52
Extremal point      53 57 317 321 325 327 330 331 350 353 405 425 464 117 120
Face      319 321 355 369 372 373 385 432 436 440 447 449 450 454 455 464 122 123 131—136 139 230 231 339
Face, stable      333 334 353 354—356 373 378 301
Factor      71 127 142 151 267 277 305 310 312 355 356 358 423 446 448
Factor, finite      134
Factor, hyperfinite      137 142 150 151 305
Factor, infinite      148
Factor, Krieger      142 151
Factor, purely infinite      148
Factor, semifinite      148
Factor, state      see “State factor”
Factor, type $III_{0}$       150 151
Factor, type $III_{1}$       150 151 231
Factor, type $III_{\lambda}$       150 151
Factor, type $II_{1}$       148 305
Factor, type $II_{\infty}$       148 150 305
Factor, type $I_{n}$       148
Factor, type I      148 355 356
Factor, type II      148 150
Factor, type III      134 148—151 421 464 132 226
Falk and Bruch      221
Fannes and Verbeure      221 222 445 446
Fell      459
Feller      303
Fermi gas      4 45—61 76 113 119 161 176 197 237 354 355 387 403 415 421 423 443
Fermi gas, sea      54
Fermi gas, surface      54 176
Feynman      232 452
Feynman — Kac formula      370 372 384 385 448 449 453
Feynman, integrals      450
Field(s)      10 308
Field(s), algebra      197 198 201 218
Field(s), construction theory      232 440 442
Field(s), Euclidean      444
Field(s), Euclidean, external (magnetic)      304 314 315 318 330 332 336 339 345 349 438—442
Field(s), relativistic      3 461 223 409
Field(s), system      197 198 201 204
Fisher      443
Fock      8 197
Fock space      see “Space Fock”
Form, bilinear      93 94 102 18 19 23
Form, closable      26 55
Form, closed      26—30 55
Form, positive      26—30 55 73 355
Form, quadratic      26—30 51—58 73 342 356- 444 457
Form, sesquilinear      214 270 26 40 60 78 93 334 406 436
Form, sum      361 363
Form, symmetric      17 22
Form, symplectic      23
Fortuin, Ginibre and Kasteleyn      442
Fourier analysis      25 94 241 243 244
Fourier analysis, transform(ation)      244 250 253 257 417 20 49 85 97 104 161 169 170 173 179—181 186 205 206 253 258 335 338 349 444
Fr $\ddot{o}$ hlich and Lieb      441
Fr $\ddot{o}$ hlich and Lieb and Park      454
Fr $\ddot{o}$ hlich and Lieb, Simon and Spencer      440
Free energy      270 292 295—298 302 347 436 440—443
Free energy, equilibrium      291
Free energy, mean      291 298
Free energy, minimum      211 267
Free group on two generators      463
Fresnel integral      161
Friederichs      9 217
Friederichs, extension      104
Fujii, Furuta, and Matsumoto      313
Fukamuja      152
Fukamuja, Misonou, and Takeda      460
Full family of states      220 221 222 305
Function(al) analysis      152 267
Function(al) analysis, Hermitian      216—218 222 223 305 368
Function(al) analysis, integration      355 358 394 443 454
Function(al) analysis, linear      42
Function(al) analysis, multilinear      39
Function(al) analysis, normal      76 146 384
Function(al) analysis, number      36 52 396
Function(al) analysis, positive (linear)      48 51 76 145 339 346 360 368 369 370 418 88
Function(al) analysis, sesquilinear      57
Function(al) analysis, tangent      174—176 182 234 297—299 443
Function(al) analysis, truncated      39—44 149 151 154 182 219 233
Function(al) analysis, Wightman      463
Function, affine      66 319 321 325 327 330 336—349 364 37 288 290 301 345
Function, almost periodic      400 401 430 435 436 464 36
Function, analytic      91 76 79—83 85 97 124
Function, Borel      5 295
Function, concave      326 328 336 99
Function, convex      321 325—327 331—333 353 355 377 80 94 297 299
Function, countably additive set      321
Function, lower semi-continuous      377 37 91 110 159 396
Function, of positive type      463
Function, subadditive      65 329 336 337
Function, superadditive      336 337
Function, trigonometric      430
Function, upper semicontinuous      326—328 331 332 338 274 275 288 301 347 365
Functionals, disjoint positive linear      370
Functionals, ordering of      52
Furuta      313
G-Abelian      381 385 386 392—395 397 405 414 415 418 419 427 433 434 462 44 45 51 133 139—144 231 339
G-Central      381 387 392—398 403 462 120 122 231
Gallavotti and Pulvirenti      311
Gallavotti and Pulvirenti and Miracle — Sole      436 437

Gallavotti and Pulvirenti, Miracle — Sole and Robinson      438
Gallavotti and Pulvirenti, Miracle — Sole and Ruelle      427
Garding      9
Garding and Wightman      224
Garrison and Wong      221
Gauge automorphisms      197
Gauge automorphisms, invariance      197 392 402
Gauge automorphisms, transformations      39 43 202
Gaussian domination      440 441
Gelfand      3 7 16 152 153
Gelfand isomorphism      64
Gelfand transform(ation)      63 250 126 142
Generator (infinitesimal)      162 165 172 206 233—244 265—279 288 290 304 24 37 89—92 96 101 110 144 146 159 164 211 244 245 249
Generator (infinitesimal), strong      168
Generator (infinitesimal), weak      168
Generators, neighboring      202
Gibbs      12 4 430
Gibbs condition      259—317 342 432 433
Gibbs state      see “State Gibbs”
Ginibrc      464 390 440 442 443 453 454
Glimm      152
Glimm and Jaffe      304
Glimm, Jaffe and Spencer      440 422
Godement      463
Golodets      232
Golodets, Gorini, Kossakowski and Sudarshan      224
Gram — Schmidt orthogonalization procedure      442 18
Graph (of an operator)      170 186 187 188 207
Graph convergence      186 187
Graph limit      187 188 281 266 371 372
Graph, Hilbert Space      278
Greenberg      437 438
Green’s functions      86 220 338 339 354 373 374 380 389 395 403 410 411 421 449 452 459
Green’s functions, compensating      374 394
Griffiths      440 442
Grothendieck      305
Group of translations      251
Group, $C_{0}$       164 169 174 202 204—206 233 248 305
Group, $C_{0}^{*}$       183 202 204—206 233 245 247 290
Group, amenable      142 401 462 463
Group, character      249 250 407
Group, circle      139
Group, compact abelian      430
Group, countable      142 419
Group, cyclic      413 419
Group, discrete      142 437 455
Group, dual      137 139 165 249 407 412 428 455 204
Group, euclidean      404
Group, finite (abelian)      141 465
Group, gauge      197
Group, locally compact      136 463 465 132 140
Group, locally compact abelian      139 249 254 310 400 401 407 408 414 417 419 424 429 431—436 455 462—464 34
Group, locally compact soluble      463
Group, modular automorphism      see “Modular automorphism”
Group, noncompact semisimple Lie      463
Group, one-parameter      12 13 96 97 159 209—299 4 8 77 84 86 109 111 114 145—150 209—212 243—247 254 282 306 310 311 427 445 446 460
Group, permutation      6
Group, perturbed      247 430 150
Group, Poincar $\acute{e}$       404
Group, quotient      424—430 437
Group, second countable      455 456 465
Group, stabilizer      413
Group, symmetry      209 404 423 424 429
Group, unitary      97 189 250 253 257 261 291 301 302 421 8 24 30 50 84 88 103 130 147 150 170 180 198 334 345 409 412 413
Gruber      459
Gruber, Hinterman and Merlini      442
Guenin      231
Guerra, Rosen and Simon      444
Guichardet      152 462
G_{\Gamma}$-abelian      414 415 417 419 420 428 434 436 455 463
Haag      9 11 13 14 156
Haag and Kastler      218
Haag and Trych — Pohlmeyer      233
Haag, Hugenholtz and Winnink      211 220 227
Haag, Kastler and Trych — Pohlmeyer      233
Haagerup      155 305 311
Hamiltonian      see “Operator Hamiltonian”
Hardy, Littlewood and Polya      460
Heisenberg      3 223 419
Heisenberg anisotropic model      243 319 333 440 441
Heisenberg isotropic model      243
Heisenberg model      243 258 334 337 338 348 350 422 424 427 440 443
Helium      56
Herman      304 306 311
Higuchi      441 442
Hilbert — Schmidt norm      282
Hilbert’s sixth problem      16
Hill      437
Hille and Phillips      303
Hoekman      233
Hohenberg      440
Huang      220
Huber      435
Hugenholtz      13 464 221 227
Ideal gas      45 46 56 421 426
Ideal, Jordan      8
Ideal, left      23 40 146
Ideal, right      23 39
Ideal, two-sided      23 24 78 133 310 352 427 454 16 84
Identity      7 21 23 25
Identity, approximate      23 39 40 41 49 56 62 78 121 153 253 353 98 99 143 184
Ikunishi and Nakagami      308
Indecomposability      14
Index set      120 129
Inequality, Bogoliubov      329 331 433
Inequality, Cauchy — Schwarz      49 50 57 78 131 173 234 422 87 96 98 162 221 334 335 416
Inequality, correlation      see “Correlation inequality”
Inequality, generalized Schwarz      213 232 222—224
Inequality, Golden — Thompson      278
Inequality, Kadison’s      305
Inequality, Peierls — Bogoliubov      278 317
Inequality, product      20
Inequality, triangle      20 132 253 272 274
information      267 435
Information theory      432
Infrared bounds      319 337 440 441
Infrared bounds divergence      170
Interaction, across a surface      249
Interaction, anti-ferromagnetic      331 332
Interaction, attractive      220
Interaction, classical      242 258 260 345 427 429 441
Interaction, coulomb      364 365 447 454
Interaction, energy      251
Interaction, exponentially decreasing      257
Interaction, external      3 263
Interaction, ferromagnetic      330 331 339 346
Interaction, finite range      241 248 251 267 437 438
Interaction, Heisenberg      335
Interaction, Ising      257 259 321 324 333
Interaction, long-range      261 413 414 442
Interaction, lower semi-bounded      360 366
Interaction, nearest-neighbour      319 330 332 345 438 439
Interaction, of a spin system      241 244 247 250
Interaction, one-body      243 248 310 313 314 319
Interaction, positive      383 388 393 401 453
Interaction, repulsive      220 414 461
Interaction, stable      364 390 394 446
Interaction, superstable      364 453
Interaction, translationally (or $\mathbb{Z}^{\nu}$ -) invariant      242 251 256 290 296 300 331 338 364
Interaction, two-body      243 248 251 256 338 364 426 422 447
Invariance condition      230 232 375
Involution      19 42 45
Irreducibility, algebraic      154
Irreducibility, topological      47
Ising      424 438
Ising model      243 257 319 320 329 339 422—427 439—443
Isometry (of a C*-algebra)      211
Isometry, partial      38 110 135 292 302 396
Isomorphism      43 44 78 228 341 348 355 369 385 390 405 425 433 444 445 452 15 19 21 83 111 158 175 203
Isomorphism order      211 213 229

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