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Operator algebras and quantum statistical mechanics 1 : C*- and W*-algebras, symmetry groups, decomposition of states

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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  • "Equilibrium states models in quantum statistical mechanics"
  • "Operator algebras and quantum statistical mechanics 1"
  • "C*- and W*-algebras, symmetry groups, decomposition of states"

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  • "In this chapter, and the following one, we examine various applications of C*-algebras and their states to statistical mechanics. Principally we analyze the structural properties of the equilibrium states of quantum systems con sisting of a large number of particles. In Chapter 1 we argued that this leads to the study of states of infinite-particle systems as an initial approximation. There are two approaches to this study which are to a large extent comple mentary. The first approach begins with the specific description of finite systems and their equilibrium states provided by quantum statistical mechanics. One then rephrases this description in an algebraic language which identifies the equilibrium states as states over a quasi-local C*-algebra generated by sub algebras corresponding to the observables of spatial subsystems. Finally, one attempts to calculate an approximation of these states by taking their limit as the volume of the system tends to infinity, the so-called thermodynamic limit. The infinite-volume equilibrium states obtained in this manner provide the data for the calculation of bulk properties of the matter under considera tion as functions of the thermodynamic variables. By this we mean properties such as the particle density, or specific heat, as functions of the temperature and chemical potential, etc. In fact, the infinite-volume data provides a much more detailed, even microscopic, description of the equilibrium phenomena although one is only generally interested in the bulk properties and their fluctuations."
  • "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."@en
  • "This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space."

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  • "Electronic books"
  • "Electronic books"@en

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  • "Operator algebras and quantum statistical mechanics. 1, C*- and W*-algebras, symmetry groups, decomposition of states"
  • "Operator algebras and quantum statistical mechanics 1 : C*- and W*-algebras, symmetry groups, decomposition of states"@en
  • "Operator algebras and quantum statistical mechanics. 1, C* - and W*-Algebras symmetry groups decomposition of states"
  • "Operator algebras and quantum statistical mechanics. 1, C - and W - algebras symmetry groups decomposition of states"
  • "Operator algebras and quantum statistical mechanics. 1 : C*- and W*- algebras, Symmetry groups. Decomposition of states"
  • "Operator algebras and quantum statistical mechanics. 1, C*- and W* - algebras symmetry groups decomposition of states"
  • "Operator algebras and quantum statistical mechanics / Vol.1, C* and W* algebras, symmetry groups, decomposition of states"@en
  • "Operator algebras and quantum statistical mechanics. 1, C*- and W*-algebras symmetry groups decomposition of states"
  • "Operator algebras and quantum statistical mechanics. 1, C *- and W *-algebras, symmetry groups, decomposition of states"
  • "Operator algebras and quantum statistical mechanics equilibrium states. Models in quantum statistical mechanics"@en
  • "Operator algebras and quantum statistical mechanics. 1, C*- and W*- algebras, symmetry groups, decomposition of states"
  • "Operatornye algebry i kvantovaâ statističeskaâ mehanika : C*- i W*- Algebry gruppy simmetrij razloženie sostoânij"
  • "Operator Algebras and Quantum Statistical Mechanics : Vol.: 1 : C ̄and WĀlgebras, Symmetry Groups, Decomposition of States"
  • "Operator algebras and quantum statistical mechanics. 1, C- and W- algebras, symmetry groups, decomposition of states"
  • "Operator algebras and quantum statistical mechanics. T. 1 : C*- and W*- algebras, symmetry groups, decomposition of states"
  • "Operator algebras and quantum statistical mechanics / Dl. 1, C*- and W*-algebras, symmetry groups, decomposition of states"
  • "Operator algebras and quantum statistical mechanics / 1, C*- and W*-Algebras, symmetry groups, decomposition of states"
  • "Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics"
  • "Operator algebras and quantum statistical mechanics"@it
  • "Operator algebras and quantum statistical mechanics"@en
  • "Operator algebras and quantum statistical mechanics"
  • "Operatornye algebry i kvantovaja statističeskaja mehanika : C [ast] - i W [ast] -algebry, gruppy simmetrij, razloženie sostojanij"
  • "Operator algebras and quantum statistical mechanics 1 : C[asterisk]- and W[asterisk]- algebras, symmetry groups, decomposition of states"@en
  • "Operator Algebras and Quantum Statistical Mechanics 1 : C*- and W*- Algebras, Symmetry Groups, Decomposition of States"
  • "Operator algebras and quantum statistical mechanics. 1, C Stern- and W Stern-algebras, symmetry groups, decomposition of states"
  • "Operator algebras and quantum statistical mechanics 1 : C*- and W*-algebras symmetry groups decomposition of states"
  • "Operator algebras and quantum statistical mechanics. [Vol.] 1, C* - and W*-Algebras symmetry groups decomposition of states"
  • "Operator Algebras and Quantum Statistical Mechanics. Vol. 1"
  • "Operator algebras and quantum statistical mechanics. 1"
  • "Operator algebras and quantum statistical mechanics. [Vol. ] 1, C* - and W*-Algebras symmetry groups decomposition of states"
  • "Operator algebras and quantum statistical mechanics 1 : C*- and W*- algebras symmetry groups decomposition of states"
  • "Operator Algebras and Quantum Statistical Mechanics 1 C*- and W*-Algebras Symmetry Groups Decomposition of States"
  • "Operatornye algebry i kvantovaja statističeskaja mechanika : C*- i W*-algebry gruppy simmetrij razloženie sostojanij"
  • "Operator algebras and quantum statistical mechanics. 1, C [ast] and W [ast] -algebras, symmetry groups, decomposition of states"
  • "Operatornye algebry i kvantovaâ statističeskaâ mehanika"

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