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

Isomorphism, anti      211
Isomorphism, Borel      295 435 465
Isomorphism, Jordan      211 213
Isotonic family (of *-algebras)      410 411
Israel      434
It $\hat{o}$ and McKean      448
J ${\o}$ rgensen      304 459
Jacobs      435
Jacobson and Rickart      305
Jadczyk      463
Jaffe      304
JORDAN      7
Jordan and Wigner      217 428
Jost      435
K $\ddot{o}$ the      154
Kac      220 452
Kadanoff and Baym      220
Kadison      78 152 154 155 305 306 311
Kadison and Ringrose      312
Kaplansky      152 153 305 307
Kastler      14 461—464 233 234
Kastler and Robinson      461 465
Kastler, Robinson and Ruelle      459
Kato      152 304 233 446
Katz      232
Kelley      152
Kelley and Sherman      442
Kernel      43 79 151 83 117 373 371 373 446
Kirkwood and Salzburg      437 438
Kishimoto      156 304 306 311 231 427 461
KMS condition      13 284 5 48 59 62 102 114—129 145—153 166 167 178 210 220—222 259 282 294 297—300 307 329 405 408 436
Kolmogorov — Sinai invariant      433
Kramers and Wannier      436—439
Kubo      13 220
Kubo — Mari scalar product      93
Kurtz      304
Landau and Lifschitz      220
Lanford      152 227
Lanford and Robinson      436
Lanford and Ruelle      462 431 432 441
Laplace transform      166 169 276
Lattice      323—325 108 239—350 419—427
Lattice gas      243—347 239—352 422-427
Law of Large Numbers      267
Lebowitz      442
Lee and Yang      439 442
Lenz      424
Lewis and Pule      220
Lieb      439
Lieb and Liebowitz      454
Lieb and Robinson      427
Lieb and Ruskai      433
Lieb, Schultz and Mattis      422
Lindblad      224
Lindenstrauss, Olsen and Sternfeld      464
Linear response      95
Lumer and Phillips      303
M ${\o}$ ller morphism      162 167 169 175 192 195
M ${\o}$ ller morphism, matrix      163 169 170 173 233 236
MacGibbon      458
Mackey      16 465
Magnetism      424
Magnetism, anti-ferro      318 334 353
Magnetism, ferro      306 315 318 333 337 424
Magnetism, para      306 314
Magnetization, spontaneous      306 318 331 334 336 337 345
Manifold, differentiable      159
Manuceau      225
Map, affine      210 216 218 221 222 369 387 464 162
Map, Borel      294 295 298 299 456
Map, completely positive      223—229
Map, contractive      341
Map, faithful      364—366
Map, invertible      219
Map, positive      209 211 215 219 229 232 341 222 223
Map, quotient      295 424 456
Map, restriction      357 358 460
Martin      13
Martin and Schwinger      220
Matrix units      253 255 308 311 312 343
Matsumoto      313
Maximum Modulus Principle      79 81
Mayer      435
Mayer and Montroll      435
McIntosh      307
Mean      379 388 400 462 163
Mean invariant      280 302 313 400 414 415 421 422 429 435 436 455 457 463 36 44 52 163 193 256 296
Measure of bounded variation      97
Measure, $\sigma$ -finite      75 184
Measure, Baire      213 322 375 433 440 450 88 91 96
Measure, barycentric      318
Measure, Borel      97 103 321 322 340 341 350 370 452 187 368 369 375 444
Measure, central      370—372 460 461
Measure, Dirac (or point)      319 3 22 323 343 456
Measure, ergodic      14 433
Measure, functional      375 377 380
Measure, Gaussian      456
Measure, Gibbs      445
Measure, Haar      137 249 289 428 435 437 438 455 463 137 142 211 217
Measure, Lebesgue      380 51 182 191
Measure, maximal      318 325—327 330—338 343 355 356 359 361 363 377 386 117 120—122 131 136
Measure, maximal orthogonal      339 359 361 395 440 460
Measure, orthogonal      320 339—462 117 143
Measure, probability      13 83 318 319 335 359 387 424 434 458 96 135 266 369
Measure, projection-valued      5 250 261 407 421 188
Measure, Radon      321 322 326 347 356 425 88 124 367—369 375
Measure, regular      321 322 332 340 341
Measure, Riesz      350
Measure, signed      323
Measure, simplicial      343 364 365
Measure, standard      440—449 452 455 465
Measure, subcentral      370—372 390 122
Measure, unique maximal      318 334 335 337 363 366 377 382 385 390 419 432 433 458 119
Measure, Wiener      367—379 386 387 448—450
Mechanical work      212 213 216
Mechanics, classical      159 287 288 289 311 365
Mechanics, matrix      3
Mechanics, quantum      3 5 6 16 121 154 159 3 217 237
Mechanics, statistical      6 10 13 16 84 124 129 273 306 311 461 3 4 113 217 237
Mechanics, wave      3
Mermin and Wagner      440
Messager and Miracle — Sole      441
Mini-max principle (theorem)      55 365 393 394 448
Minkowski space      369
Misonou      460
Mixing      14 393 41 177 422
Mixing, strong      401—403 42 62 320
Mixing, weak      423 455 465
Miyadera      303
Modular automorphism (group)      86 96 97 147 149 230 278 279 281 84 114 124—128 151 221 277 430
Modular condition      83
Modular conjugation (involution)      89 94 102 226 227 278 391 397 107 118 125 160 194 283
Modular function      137
Modular operator      89 91 94 96 102 103 226 227 229 278 283 285 391 403 86 107 118 125 160 161 187 194 283 404
Modular theory      83 78 85
Modulus (of an element)      34 38
Mokobodski      458
Momentum      4 36 53 54 62 346 350
Montroll      438
Morphism      42 213 224 227 228 341 342 390 450 451 162—166
Morphism, anti      211 213 224 227 228
Morphism, Jordan      209 211
Murray      3 11 16 154
Nagel      463
Nagumo      303
Nagy      152 304
Naimark      3 7 16 152 153 305
Nakagami      308
Nambu      427
Naudts and Verbeure      221

Naudts and Verbeure, Nearest-neighbour(s)      327—331 421 448
Naudts and Verbeure, Verbeure and Weder      221 225
Nelson      304 448
Net      39 119 123 323 326 336 337 342 379 383 386 388 392 396 403 415 463 108 122 240
Net of subalgebras      118 121 123
Net, decreasing      118 119
Net, increasing      76 78 79 130 146 155 30 72 281
Neumann series      26 171 241 268 274
Newton      233
Nondegenerate      72
Norm      20
Normal subgroup      424 428 429 440 463
Novikov      449 451
Observable      5 6 7 12 160 209 370 461 462 3 6
Observable algebra      137
Observables, algebra of      12 122 141 159 4 197 198
Olesen      309
Olesen and Pedersen      226
Olsen      464
Onsager      439 448
Onsager — Yang      439
Operator, adjoint      19
Operator, affiliated with an algebra      87 90 287 116
Operator, annihilation      8—12 17 23 27 37 45 58 148 161 217 226 258 398 425 426 444
Operator, antilinear      86 88 16
Operator, antiunitary      84 87 89 210 226 248
Operator, bounded      20 160 173 197 203 205 348 378 409 415 418 7 11 14 16 33 87 145
Operator, closable      88 177 187 235 267 271 276 8 13 24
Operator, closed      87 91 170 171 177 197 235 276 348 25
Operator, compact      21 72 129—131 210
Operator, conjugation      84
Operator, conservative      174 265
Operator, creation      252 257 8—12 17 23—27 45 58 148 161 217 226 258 398 426 445
Operator, decomposable      443—445 448 453
Operator, diagonalizable      443—448 451 455
Operator, dissipative      174 177 193 196 197 235 290 303 304 306 90 245
Operator, double difference      349
Operator, essentially self-adjoint      272 278 289 8 12
Operator, finite-rank      210
Operator, Hamiltonian      4 12 159 163 273 4 36 45—48 52 57 65 151 196 241 349—365 390 411 426 428 450 455
Operator, Laplacian      188 48 49 54 60 78 355 372 426 445 446
Operator, lower semi-bounded      5 51 61 63 351 361—363 410
Operator, lowering      252
Operator, modular      see “Modular operator”
Operator, negative part of an      34
Operator, normal      292
Operator, number      4 7 10 25—37 218 363 425 442
Operator, positive      57 76 89 104 273 351 26—29 31 40 60 73 78 114 135 208 341
Operator, positive part of an      34
Operator, raising      252
Operator, self-adjoint      5 6 89 104 153 182 240 269—271 273 277 280 291 25—30 36 40—48 57—60 73 76 78 84 104 276 341 352 356—366 410 431
Operator, shift      252 257
Operator, skew-adjoint      292
Operator, spin lowering      257 258 319 425 428
Operator, spin raising      257 258 319 425 428
Operator, symmetric      104 182 238 240 246 269 272 278 8 13 54 208 357 428
Operator, trace-class      6 68 76 129 5 46—48 57—59 219 220 363—365 410 411
Operator, unbounded      5 153 463 60 116
Operator, unitary      8 47 57 159 210 225—227 240 247 248 269 293 295 374 13 19 21 61 90 127 142 164 406 407
Operator, Weyl      8 11 14 18 19 30 35 57—60 73 417 442
Operators, measurable family of      442 443
Orbit      141 142 425 429 430 434—438 165
Order, anti-symmetric      39 325
Order, reflexive      39 325
Order, relation      36 39 318 325—327 334—336 346 348 349 359 424 458 27
Order, structure      78
Order, transitive      39 325
Ornstein      435
Orthogonality relation      12
Oscillator, harmonic      36
Ota      306
Paige      7
Parseval’s equality      245
Partial order      325
Passive system      217
Path      367—376 390 452
Pauli (exclusion) principle      9 12 447 454
Pauli (exclusion) principle, matrices      337 241 310 319
Pedersen      152 305 309
Peierls      415 439 440
Peierls argument      319 439 440 445
Period, approximate (or s-)      430
Perturbation      160 171 184 193 202 290 95 145—149 164—169 176 194 196 212—215 261-263 316 333 350 358—363 446
Perturbation series (expansion)      195 196 311 94 146 149 150 153—165 232 308—314
Perturbation, bounded      194 202 204
Perturbation, relatively bounded      193 207 363
Phase      10 51 339
Phase separation      3 345 426 443
Phase space      288
Phase transition      10 3 237 306 324 338 404 439—445
Phase, pure      374 462 113 118 119 144 289 304 422 445
Phillips      303
Planck’s constant      4
Polarization identity      38 67 182
Potential Coulomb      359 448
Potential Coulomb, positive      364 394 395 459
potential energy      356—359 386 424
Potential energy, -body      358 359 458
Potential energy, finite range      394
Potential energy, Lennard — Jones      359 360
Potential energy, transiationally invariant      358 390 394
Potential energy, two-body      358 390 395 414
Poulsen      464
Powers      156 306 225
Powers and Sakai      311
Predual      69 75 83 216 233 280 294 299 446
Pressure      53 54 270 387 393 443 445 450—454
Projection, final      110
Projection, finite      147
Projection, infinite      147
Projection, initial      110
Projections, equivalent      147
Propagation velocity      252—257
Pseudosupported      318 322 331 367 372 373 377 138
Pulvirenti      311
Pusz and Woronowicz      232 237 429
Radius of analyticity      178
Radon — Nikodym derivative      90
Range (of an interaction)      242 258
Range (of an interaction), finite      258
Range, numerical      292 302 312
Ray      159 210
Reduced density matrices      381—400 414 450
Reduced density matrices, truncated      393
Reed and Simon      152 304 452
Reflexive Banach space      206
Regularization      308
Relative modular operator      278 281
Representation      42 23
Representation, associated with a state      57 55 55 132 349
Representation, covariant      136—138 133 204
Representation, cyclic      14 45 56 57 60 353 358 375 60 82 84 88 130 139 170 179 335 405
Representation, factor      see “Factor”
Representation, faithful      8 14 43 44 79 133 138 139 220 237 238 272 310 352 199 204 210
Representation, Fock — Cook      8 11 25 30 33—37 52 217—220 350 446
Representation, group      155 374
Representation, irreducible      8 47 57 80 151 211 224 352 368 393 394 448 463 34 142 168 204 218
Representation, isometric      8
Representation, multiplier      20
Representation, non-degenerate      45 80 446 448
Representation, normal      79
Representation, regular      21 33—36 148 204 208
Representation, Schr $\ddot{o}$ dinger      6 8 9 34—36 435
Representation, space      43
Representation, sub      44 81
Representation, uniformly bounded      254 256
Representation, unitary (group)      3 5 250 251 379 383 400 403 407—409 412 415 419 421 422 426 429 430 464 6 7 20 98 129 141 144 169 204
Representations, direct integral of      449 450
Representations, direct sum of      81 319 339
Representations, disjoint      370

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