Operator Algebras and Quantum Statistical Mechanics: Equilibrium States. Models in Quantum Statistical Mechanics

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Springer Science & Business Media, Jan 1, 1997 - Mathematics - 517 pages
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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.
  

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Contents

51 Ιntroduction
3
52 Continous Quantum System I
6
522 The CAR and CCR Algebras
15
523 States and Representatives
23
524 The Ideal Fermi Gas
45
525 Τhe Ideal Bose Gas
57
53 KMSStates
76
532 The Set of KMS States
112
623 The Maximum Entropy Principle
266
624 Translationally Invariant States
286
625 Uniqueness of KMS States
306
626 Nonuniqueness of KMS States
317
627 Ground States
338
63 Continuous Quantum Systems II
353
631 Τhe Local Hamiltonians
355
632 Τhe Wiener Intergral
366

533 The Set of Ground States
131
54 Stability and Equilibrium
144
542 Stability and the KMS Condtion
176
543 Gauge Groups and the Chemical Potential
197
544 Passive Systems
211
Note and Remarks
217
Models of Quantum Statistical Mechanics
235
61 Introduction
237
62 Quantum Spin System
239
622 The Gibbs Condition for Equilibrium
261
633 Τhe Thermodynamic Limit I the Reduced Density Matrices
381
634 The Thermodynamic Limit II States and Greens Functions
395
64 Conclusion
422
Notes and Remarks
424
References
463
Book and Monographs
465
Articles
468
List of Symbols
487
Subject Index
499
Copyright

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Selected Papers of M. Ohya
Masanori Ohya
No preview available - 2008
Spinors in Hilbert Space
Roger Plymen
No preview available - 1994
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