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

Abragam and Proctor      220
Absolute value      34
Action, continuous      393 400
Action, dual      140 149 375
Action, ergodic      137 142
Action, free      137 142
Action, transitive      464
Activity      47 63 64 70 383 384 389—392 395 401—403 421 429 442
Adjoint      19
Aizenman      440 441
Akemann      460
Akemann and Pedersen      309
Albert      7
Albeverio and H ${\o}$ egh — Krohn      449
Alfsen      8
Algebra, -dimensionally homogeneous      351 459 460
Algebra, $\mathcal{LC}(\mathfrak{H})$       21 72 129—133 246 247 306 307 309 352 4 5
Algebra, $\mathcal{L}(\mathfrak{H})$       20 38 68—72 85 96 106 124 129 131 225 226 245—248 258 305 306 309 321 356 379 398 4
Algebra, $\sigma$ -finite von Neumann      84 151 155
Algebra, abelian      19 35 58 62 83
Algebra, antiliminal      352
Algebra, approximately finite      233
Algebra, at infinity      122 123 126 156 318 373 440 453 454 205
Algebra, B      152
Algebra, Banach      19 20 25 137 152 430
Algebra, Borchers      463
Algebra, C      3 19 20 25
Algebra, commutant      122 126 370
Algebra, commutative      19 21 61 154
Algebra, direct integral      445 446
Algebra, finite von Neumann      147
Algebra, fixed point      310 313
Algebra, function      21
Algebra, group      249
Algebra, hyperfinite von Neumann      150 151
Algebra, infinite von Neumann      147
Algebra, Jordan      7 16
Algebra, local      11 118
Algebra, maximal abelian von Neumann      320 350 361 367 391 417 420 447 448 452
Algebra, multiplier      309
Algebra, normed      20
Algebra, nuclear      144 151 232
Algebra, operator      3 136 439
Algebra, prime      310
Algebra, properly infinite von Neumann      135 141 147
Algebra, purely infinite von Neumann      147
Algebra, quasi-local      11 81 118—129 133—135 219 289 317 321 352 373 450 453 454 460 5 16 22—25 41 63 118 177 239 240 244 259
Algebra, quotient      39 40 41 43
Algebra, reduced von Neumann      155
Algebra, self-adjoint      19
Algebra, semifinite von Neumann      147 148 150
Algebra, semisimple      306
Algebra, simple      7 24 44 133 134 142
Algebra, topological      7
Algebra, type I C      151
Algebra, UHF (Uniformly hyperfine)      129 156 268 306 307 308 351 353 17 229 239 246
Algebra, von Neumann      3 65 70 75 76
Algebra, W      3 155 305
Algebra, Weyl      30 35 37 38
Algebras, measurable family of      445
Analysis, abelian harmonic      140
Analytic continuation      25
Analyticity, strong      99 155 178
Analyticity, weak      90 155 178
Angelescu and Nenciu      450 452
Annihilator      408 412 417 429 436 455 22 204
Approximation theory      202 290 299 304
Araki      152 155 156 219—222 226—229 432 436—439
Araki, and Ion      431 432
Araki, and Kishimoto      234
Araki, and Lieb      435
Araki, and Sewell      222 436 437
Araki, and Shiraishi      220
Araki, and Stermer      231
Araki, and Woods      220
Araki, and Wyss      220
Araki, Haag, Kastler and Takesaki      234
Arima      449
Arnold and Avez      463
Arveson      152 308 309
Asymptotic abelianness      14 340—343 380 406 414 461 463 40 43 144 163 174—183 195 198 210 240 303 320 326 422 423
Asymptotic, $L^{1}(\mathfrak{U})$       163—168 176—181 188 198- 236
Asymptotic, weakly      403 132
Australia      442
Auto-correlation, lower bound(s)      91 92 94 96 108 109 113 159 227 283 286 333 437
Auto-correlation, upper bound(s)      94—97
Automorphism      12 13 16 44 56 96 97 102 108 139 209—313 374—452 4 15—19 40—43 51 57—63 73-85 109—113 189 195 214 243- 306 321 331 414 436
Automorphism, anti      209 211 221
Automorphism, inner      141 148 149 225 249 283 293—295 300 305 310 312 313
Automorphism, Jordan      211 212 218 219 222 224—227 229—231 277
Automorphism, modular      see “Modular automorphism”
Automorphism, order      211 225
Avez      464
Babbitt and Thomas      442
Baire measure      see “Measure Baire”
Baire set      318 322 324 331—333 350 353—357 367 458 137 138 367
Baire structure      352
Balslev      219
Banach      154
Barycenter      318—350 359—390 424 426 433 440 450 458 117 119 135 306
Base (of a cone)      334
Batty      231
Bauer maximum principle      331 293 301
Baumann and Jost      435
Berman, Bruch and Fortune      221
Bethe      442
Bicommutant      72
Bidual      130 217
Billingsley      435
Birman and Kato      233
Bishop and de Leeuw      458 459
Bishop and Phelps      436
Bloch      453
Bogoliubov      218 221
Bogoliubov and Khatset      437
Bogoliubov automorphism      197
Bogoliubov scalar product      93
Bogoliubov transformation      16—21 41—51 73 77 99 148 161 164 218 219
Bohr      3 430
Bohr compactification      435 436
Boltzmann      4
Boost      302 309
Borchers      308 309 311 312
Borchers and Yngvason      463
Borel automorphism      288
Borel cross section      295
Borel function      5 295 187 377
Borel map      see “Map Borel”
Borel measure      see “Measure Borel”
Borel set      5 289 295 318 322 331 333 340 343 350 354—357 412 460 463 186 367 377 379 380
Borel structure      350 440 446 362
Bose gas      14 56—75 197 198 218 220 237 353—420 442 459-461
Bound, greatest lower      323 334 335 385 117
Bound, least upper      76 78 79 121 323 369 385
boundary conditions      160 3 48 63 74 146 147
Boundary conditions, classical      51 54 62 355 363 392 444 446
Boundary conditions, completely absorbtive      376
Boundary conditions, completely reflecting      376
Boundary conditions, Dirichlet      55—57 64—70 356 363 374- 379 386—393 396 401 402 414 444 448—455
Boundary conditions, elastic      56
Boundary conditions, free      444
Boundary conditions, Neumann      53 55—57 373 376 389 393 451
Boundary conditions, periodic      55 64 380 444
Boundary set      326 327 330 331 353
Bourbaki      151
Boyle’s law      54
Bratteli, and Haagerup      311
Bratteli, and Kastler      233
Bratteli, and Kishimoto      304 311 428
Bratteli, and Robinson      305—307 311 453 459

Bratteli, Elliott and Herman      229
Bratteli, Elliott and Kishimoto      229
Bratteli, Herman and Robinson      304 311
Bratteli, Kishimoto and Robinson      233 442
Brownian motion      366 376 448
Brownian motion, particle      367 368 377
Brownian motion, set      306 308
Brush      424
Bucholz and Roberts      304 311
Butzer      304
C*-norm      20 22 31 143
Cannon      270
Cantor — Bernstein, argument      81
CAR algebra      14—16 23 37 42—53 77 99 148 161—169 219 225 237 350—355 395
CAR relations      6 10 11 14
Carnot’s formula      216
Cauchy estimates      178
Cauchy representation      242
Cauchy transform      25
Cayley numbers      7
CCR algebra      15 18—34 40 57—60 67 218 225 237 349 354 355 395 396 443
CCR relations      6 10—15
Center      71 123 125 126 147 295 317 370 389 390 445 446 453
Center of mass      318
Central sequence      309
centralizer      279 280 282 284
Chaiken      9
CHARACTER      61—63 139 249—251 351 430 464 130 131
chemical potential      3 5 45 197 198 204 210 211 234 396 410 414
Chernoff      303 304
Chi      306
Choquet      458—460
Christensen and Evans      224
Circled subset      98 163
Classification of C*-algebras      145 151
Classification of factors      145
Cluster property      118 128 156 393 398 401 404 406 420 429 438 440 42 106 118 163 178 185 194 198 201 218 423 437
Cluster property, multiple      402
Cocycle      141 298 312 131 145—148 157 212 287 316
Cocycle, identity      294 297
Cocycle, one      294 296 299
Cocycle, two      296 297 299
Cohomology      312
Cohomology of $\mathbb{R}$ is trivial      307
Commutant      47 57 58 71 85 305 317 320 339 370 375 426 431 433 445 11
Commutation relations, canonical      4
Commutation relations, Weyl      6
Commute strongly      278 279 107 108 116 191
Condensation, Bose — Einstein      63 64 70 78 353 354 403 440
Conditional expectation      150
Conditional measure, Wiener      368
Cone, apex of      334
Cone, base of      334
Cone, causal      257 259
Cone, convex      34 36 83 334
Cone, dual      104
Cone, hereditary      145
Cone, homogeneous      156
Cone, natural      102—108 147 155 156 226—229 232 264 299 305 369 116 157 275
Cone, orientable      156
Cone, pointed      105
Cone, self-dual (self-polar)      83 84 97 104 105 145 156
Connes      155 156 308 310 312 232
Connes and Takesaki      310
Construction, GNS      153 220 407 460
Continuous, $\sigma(X,F)$       97 98 100 164—184 194 204 219 250 252—254 256 303
Continuous, $\tau(X,F)$       168 184
Continuous, H $\ddot{o}$ lder      206 290 369 370 375
Continuous, strongly      97 160 164 169 226 232 240 257 261 265 267 268 299 4 23 57—61 80 86 109 111 127 138 146 150 244—254 282 306 316 405 406
Continuous, uniformly (norm)      97 160 161 233 256 261 263 264 91 142 145 148 224 225
Continuous, weakly      97 136 160 164 169 226 87
Continuous, weekly*- ( $\sigma$ -weakly)      160 169 226 257 259 261 267 285 288 294 296 299 302 312 77 80 84 127 274
contour      321—330 440
Contraction      161 169 170 177 178 194 196 91
Convolution      249 252
Cook      8 217
Core      167 182 188 191 196 267 270 274 275 277 278 282—284 286 287 289 290 308 35 85 96 98- 182 191 265 277 286 340 365
Core hard      360 394 443
Correlation      39 40 218
Correlation, canonical      93 94
Correlation, function(al)      380—382 391 437 443 450—453
Correlation, inequality      221 222 442 443 446 454 459
Correlation, long-range      118
Courbage, Miracle and Robinson      218
Cross section      290
Cross-nomi      144
Crossed product      136—141 284 310
Crossed product, skew      141
Cuntz      306 226
Cyclic projector      46
Cyclic subset      85 86
Cyclic subspace      46
Cyclic vector      45 46 86 88 109
Dang Ngoc      234
Dang Ngoc and Guichardet      462
de Leeuw      303 304 458 459
Decomposition      14 32 45 105 106 117 121 216—218 221 275 343 379 415 424 113
Decomposition, almost periodic      430 431 433 436 437
Decomposition, at infinity      317 321 373 453 454 465
Decomposition, barycentric      321 324 335 350 356 367 447 458 461 37 114 301 302
Decomposition, central (factor)      317 358 370 423 447 460 119 143 211 227
Decomposition, direct integral      450 453
Decomposition, direct sum      45 356
Decomposition, ergodic      318 374 380 386 390 393 429 440 461 462 463 119 144
Decomposition, extremal      317 318 358 359 367 440 447 121 143 144 210
Decomposition, finite      319
Decomposition, Jordan      216 219 222 236 305 369
Decomposition, of positive linear functionals over *-algebras      463
Decomposition, of representations      317 440 446
Decomposition, of states      129 317 449 450 459 460
Decomposition, orthogonal      36 229 319
Decomposition, polar      38 72 87 89 90 92 107 108 112 116 130 152 232 279 287 291 292 302 312 396 397 27 121 275
Decomposition, property of a lattice      336
Decomposition, spatial      439 447 449 451 455 465
Decomposition, spectral      95 251 320 407
Decomposition, theory      317 319 373 413 414 440 459
Delbr $\ddot{u}$ ck and Moli $\grave{e}$ re      435
Dell’ Antonio      9 219
Dell’ Antonio and Doplicher      218
Dell’ Antonio, Doplicher and Ruelle      218
Density matrix      76 85 106 124 127—131 210 405 25 36 159 268—274 278—284 293 295 383 384
Derivation      160 233—249 265—268 282 286 292 306 307 309 4 214 244 247 249 413 427 430
Derivation, bounded      235 236 246 249 262 263 290 291 300 301 144 145 244
Derivation, everywhere defined      235 267 263 306
Derivation, implementation of a      269
Derivation, inner      305 144
Derivation, nonclosable      306
Derivation, norm-closed      235—245 306
Derivation, normal      308
Derivation, spatial      268 270—272 274 287
Derivation, symmetric      233 144
Derivation, theorem      262
Diffeomorphism      159
Differentiable, strongly      203
Differentiable, uniformly      161 162
Differentiable, weakly      203
Digernes      311
Dirac      217
Direct integral      439 440 450 454
Direct sum      45 46 60 439 357 363 364
Dixmier      152 312
Dobrushin      429 440 446 453
Doplicher and Kastler      463 464
Doplicher and Kastler, and St ${\o}$ rmer      462
Doplicher and Kastler, Kastler and Robinson      461
Douglas      460
Dual      48 51 53 62 76 130 170 203 216 219 305 317 350
Dual group      see “Group dual”
Duality      126 130 169 209 439 442
Dubin and Sewell      459

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