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

Representations, equivalent      48 370 135 139 140
Representations, inequivalent      9 168 170 218
Representations, measurable family of      447
Representative      43
Resolvent      25 27 91 165 168—170 184 306 311 175
Resolvent, convergence      184 186 188
Return to equilibrium      159 177 196
Rickart      305
Rideau      219
Rieffel      155
Riemann approximant (sum)      167 243 56 63
Riemann approximant (sum), integral      33 215 243
Riemann Lebcsgue lemma      51
Riesz and Nagy      152 304
Robbins      431
Roberts      304 311 312
Robertson      305
Robinson      304—307 311 461 464 219 220 232 427 434 440
Robinson and Ruelle      434
Rocca and Sirugue      221
Roepstorff      221
Root mean square deviation      349
Rudin      152 221
Ruelle      9 459—465 229 436—443 446 453 459
Ruskai      459
Russo and Dye      305
Sakai      76 152 155 306 307 309 311 312 459 460
Sato and Ueno      448
Saturation problem      304
Scattering theory      163 164 233 454
Schr $\ddot{o}$ dinger      3 6
Schr $\ddot{o}$ dinger equation      4 46 376
Schultz      8
Schur’s lemma      153
Schwartz      152
Schwarz reflection principle      275 81
Schwinger      13
Second law of thermodynamics      212
Second quantization      8 45 233
Sector of an operator      287 292
Segal      7—9 16 152 153 461 223 224
Semigroup      161 164—168 203 91 144 284 361 368 370 373 378 383 446
Semigroup, $C_{0}$ -      164 169—178 187—194 202 235 303 304
Semigroup, $C_{0}^{*}$ -      164 170 171 183 193—196 202 303 304 225
Semigroup, completely positive      224 225
Semigroup, dual      303
Semigroup, positively preserving      222
Semigroups, convergence of      184—192
Seminorm      65 66 163 168 174
Seminorm, $\tau(X.F)$       204
Seminorm, C      138
Separability condition S      352 353 367 377 378 426—428 432 436 447 449 450 454 455 460
Separating subset      85
Separatingvector      80 86 88 109 226—230 277—289 311—444 82 84 86 87 104 114 120 153 183 190 263 276 279 409 411
Set, $F_{\sigma}$       322 357 372 373
Set, $G_{\delta}$       322 331—333 338 357 458 133
Set, $\mu$ -measurable      356 357 452 454
Set, $\mu$ -negligible      356 357 440
Set, analytic      295 357 458 460
Set, Baire      see “Baire set”
Set, Borel      see “Borel set”
Set, convex      53 59 66 317—359 293
Set, directed      39 46 121 123 324 331 345
Set, metrizable      132 133 318 331 333 458
Set, pseudosupporting      322 331
Set, resolvent      25 28
Set, stable      331 342
Set, supporting      322 357 426
Sewell      221 222 436 437
Shale and Stinespring      219
Shannon and Weaver      435
Sherman      460
Simon      152 304
simplex      334 335 367 368 385—387 405 458 464 117 118 122 131 133 134 139 230 231 301 306 441
Simplex, Bauer      464
Simplex, Poulsen      464
Sirugue and Testard      226
Sirugue and Testard, and Winnink      227 458
Skau      458 460
Slawny      218
Smoluchowski      449
Sommerfeld      3
Space, analytic Borel      295
Space, configuration      120
Space, conjugate      70 238
Space, direct integral      439 142 449
Space, direct sum      439
Space, Fock      7 9 12 15 30 34 46 56 349 415 444
Space, measurable family of      441 442 444 447 449
Space, Polish      295 440 456
Space, quotient      23
Spectral concentration      253
Spectral projector (projection)      58 71 87 104 135 118
Spectral radius      25 26 29 31 37 44 59 241 312 22
Spectral subspace      251 252 257 259 410 142 204
Spectral theory      7 249 281 298 308 50 99 188 204
Spectral values      252
Spectrum      25—28 32 35 51 61 62 149 165 220 240 245 248 251 252 256 257 263 294 306 309 407 419 420 434 464 21 33 84 104 141 147 171 172 176 180 181 183 190 351 352 365 366
Spectrum of an abelian C*-algebra      61
Spectrum, $\Gamma$       310
Spectrum, Arveson      310
Spectrum, point      407 412 415 419 121 424 455 457 464 163
Spectrum, semi-bounded      261
Spin      7 239 241 424
Spin system      311 120 211 220 222 236—353 413 422
Spin waves      350—352
Square root      32 34 36 152 235 236 306
St ${\o}$ rmer      8 16 305 462 464 219
Stability      13 160 184 202 89 90 99 145 148 150 158 164—183 192—196 211 232 233 340 364 390 410 423 447 454
Stability, local thermodynamic      275 437
Standard form      83 155 226 228 305
State      42 48 51 153 344 345 346 350 353 358 361 363 439 452 23
State, (G-) ergodic      374 377 378 393—398 405 407 408 410 413 418 423 424 428 440 452 459—464 131—135 138 141—144 240 303
State, (G-) invariant      13 117 240 268 272 374—387 390 393 398 400 402 07 414 415 423 427 431 434 459 461 462 44 52 88 98—216 287 290 294 301- 315 333 336 345—350 422 436
State, almost periodic      414 424 430—433 422
State, analytic      39 40 382 397 402
State, bound      167
State, ceiling      97 108 113 158 168 192 197
State, centrally ergodic      395 396 202
State, chaotic      97
State, completely passive      101 226
State, equilibrium      11 12 273 3 5 40 47—88 112 118 123 148 149 158 159 176 177 198 211 218 219 237—239 260—263 286 291—294 300—315 354—363 400 422 436- 443
State, even      43 103
State, extremal G-invariant      318 121
State, factor      81 128 317 356 358 372 401 403 452 460 117—120 133 134 139 140 151 160 184 199 219 321
State, faithful      13 83 85 96 299 403 84 115 116 124—128 264 275—279
State, finite density      36 170
State, Fock      24 219
State, Gibbs      4 46—50 57—77 88—93 121 144 260—275 298 315—339 354
State, ground      9 273 277 289 309 36 54 97—113 131—141 145 158 164 168—176 192 194 197 226 227 338—351 443
State, guage invariant      44 48—50 54 59 60 68 78 100 108 169 206 210 219 348
State, KMS      285 5 48—51 75—84 88 92 97—216 221 225 237 260—264 295—297 306 308—320 330-340 354 423 437—441
State, locally normal      118 124 125 129 219 317 352 356 373 460 25 34 52 62 170 395 396 401 420
State, mixed      6
State, normal      7 9 75—83 96 129 131 210 220 238 299 355 370 371 383 390 398 452 460 462 25 30—36 76 80 115 123—126 132 151 169 170 174—176 276 337—340 341-344
State, passive      90 101 102 211 212 215
State, periodic      414 141 144 210 211 290 417 422
State, perturbed      151 159 174—177 194 211 265 276 279 316
State, physical      7 122
State, primary      81
State, pure      6 53 57 58 62 153 343 350 352 356 358 359 367 368 372 452 461 133 134 141—146 172 174 175 181 273 275
State, quasi-free      40 43 44 48—52 54 59 60 69 78 100 108 169 170 219 233 388
State, regular      23 24 29 33—37
State, trace      84 87 311 421 76 83 97 102 109—112 121 123 154 174 184 194 211 307
State, vector      49 131 356 395 133 153 160
States, disjoint      9 370 395 117 128 139—141 196
States, neighbouring      219
States, orthogonal      339 340
States, set of      7 53 59 61
Statistics, Boltzmann      384 387 391 392 395 447 450

Statistics, Bose      121 7 355 366 383—394
Statistics, Fermi      121 156 7 355 365 366 384 390 394
Sternfeld      464
Stinespring      305
Stirling bounds      431
Stirling number      401
Stone      5 16
Streater      427
Streater and Wightman      231
Strong mixing of all orders      402 403
Subadditivity      271 272—275 288
Subadditivity, strong      271 288 289 433
Subalgebra      19
Subalgebra, central      124
Subalgebra, fixed point      137 149
Subspace, cyclic      46
Subspace, invariant      44
Subspace, measurable      441
Subspace, stable      44
Summable central sequence      309
Support of a measure      318 322 376 377 427 432 435 436 437 453
Support, finite      322—330 335 337 361 371 377 432 91 118 122
Susceptibility, magnetic      318
Symmetry      136 209 374 423 424 141 239 286
Symmetry, broken      374 413 423 119
Symmetry, inner      198
Symmetry, spin reversal      321 324 325
Symmetry, Wigner      210 225 226 248 305 307
System, closed      267 294
System, isolated      267
System, open      263 291 294
Takeda      460
Takesaki      13 83 155 310 83 221 227 228
Takesaki and Tomiyama      459
Taylor series      34
Temperature      3 5 10 46 51 70 128 216 220 221 262 268 306 307 315 318 422 428 439 141
Temperature, critical      306 318 439 441
Temperature, negative      51 220
Temperature, zero      53 340 347
Tensor product      142—145 7 239 416
Theorem, Alaoglu      98
Theorem, Alaoglu — Bourbaki      53 68 154 163 176 205
Theorem, bicommutant      72 445
Theorem, Bochner      103
Theorem, Borchers — Arveson      261 263 269 309 421
Theorem, capacity      460
Theorem, Carath $\acute{e}$ odory — Minkowski      321
Theorem, Carlson’s      91 155
Theorem, Cartier — Fell — Meyer      460 122
Theorem, Cauchy      88
Theorem, closed graph      207 235
Theorem, Connes      128
Theorem, Connes — Takesaki duality      149
Theorem, Connes’ cocycle      231 232
Theorem, Connes’ Radon — Nikodym      147
Theorem, derivation      262 224
Theorem, edge of the wedge      81 83 84 99 153
Theorem, Effros      450
Theorem, Fannes — Vanheuverzwijn — Theorem, Verbeure      125
Theorem, Fr $\ddot{o}$ hlich — Pfister      331 441
Theorem, Fubini’s      257 258 137
Theorem, Goldstone’s      176
Theorem, Haag’s      140 231
Theorem, Hahn — Banach      59—61 65 66 75 101 154 174 200 218 221 325 328 329 339 360 403
Theorem, Hille — Yosida      171 173 174 178 181
Theorem, Kadison’s (transitivity)      154 402 171
Theorem, Kaplansky density      74 103 122 123 154 218 232 236 347
Theorem, Kato’s      446
Theorem, Kovacs — Sz $\ddot{u}$ cs mean ergodic      383 124
Theorem, Krein — Milman      53 59 61 153 217 163 173 201
Theorem, Krein — Smulian      98 155 341
Theorem, Lebesgue dominated covergence      100 186 412 428 437 86 87 148 166 173 179 181 184 185 371 372 401
Theorem, Liouville’s      275 79 99 113
Theorem, Lumer — Phillips      177
Theorem, Mackey — Arens      223
Theorem, Mackey’s      98
Theorem, Markov — Kakutani fixed point      415
Theorem, Mazur’s      403 464
Theorem, mean ergodic      378 383 386 391 394 398—100 411 415 421 422 462 44 162
Theorem, Minlos      455
Theorem, monotone convergence      327
Theorem, Parseval’s      180
Theorem, Perron — Frobenius      431
Theorem, Phragmen — Lindel $\ddot{o}$ f      80 99
Theorem, Pontryagin’s duality      139
Theorem, Pusz — Woronowicz      101
Theorem, Riesz representation      68 70 83 213 239 322 350 124 368 375
Theorem, Roepstorff — Araki — Sewell      91
Theorem, Roepstorff — Fannes — Verbeure      95
Theorem, Sakai’s      76 233
Theorem, SNAG (Stone — Naimark — Ambrose — Godement)      250
Theorem, Spectral      5
Theorem, Spectral Mapping      31
Theorem, Stinespring’s      223
Theorem, Stone — von Neumann uniqueness      6 33 34 218
Theorem, Stone — Weierstrass      24 63 64 325 346 347 376 387 202 207 368
Theorem, Stone’s      251
Theorem, Tauberian      250 253
Theorem, Taylor’s      398—404
Theorem, Theorem, Radon — Nikodym      213 192
Theorem, three-line      80—82 152 155 157 274
Theorem, Tomita — Takesaki      94 155 311 123
Theorem, Tomita’s      341 450 452
Theorem, Trotter — Kato      304
Theorem, uniform boundedness      100 176
Theorem, von Neumann density      72—74 154
Thermal wavelength      55 58 65
Thermodynamic limit      10 11 13 3 49—57 63 67 74 75 86 109 220 260 298 366 372 381—383 391—395 401 417 423 438 442 454
Thomas      443
Time development      160
Titchmarsh      221
Tomita      13 83 459 460 221
Tomita — Takesaki theory      13 83 84 91 146 84 104
Tomiyama      459
Tomiyama property E of      150
Topology, $\sigma$ -strong      66 70 74
Topology, $\sigma$ -strong*      69 70 74
Topology, $\sigma$ -weak      67 70 74 78 279 445 146
Topology, $\sigma(X, F)$       97 98 99 163 166 171
Topology, discrete      435
Topology, locally convex      59 65 97 163
Topology, locally uniform      132 133
Topology, Mackey ( $\tau(X,F)$ -)      98 155 163 164 167 169 174 184
Topology, metric      20 132 133
Topology, quotient      295
Topology, strong      66 70 74 108 295 145 278
Topology, strong operator      127 309 150 206 215
Topology, strong*      69 70 74 108 295
Topology, uniform (norm)      20 25 53 70 108 127 131 163 169 194 289 335 101 272 306 436
Topology, weak      67 70 74 108 295 356 190
Topology, weak operator      3 341 230
Topology, weak*( $\sigma(\mathfrak{U}^{*}, \mathfrak{U})$ -)      14 53 68 131 132 181 206 307 329 335 337 346 355 377 406 86 108 109 116 128 169 272—275 288 302 340 348 411 436
Trace      145 280 281 287 46 191 246 269 281—283 301
Trace, faithful      148 149
Trace, norm      68
Trace, normal      148 149
Trace, semifinite      148 149
Trajectory      367—381 384 386 387 394
Trajectory, composite      385 391
Trajectory, elementary      385 386 390
Transfer matrix      437—440
Translations, space      13 41—44 51 62
Translations, time      51 62
Trotter      304
Trotter product formula      304 157 225 370
Twist      206 302
Uncertainty      432 433
Urysohn’s lemma      332
VACUUM      9 37 41 44
van Daele      155 220

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