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Communications in Mathematical Physics

, Volume 5, Issue 3, pp 215–236 | Cite as

On the equilibrium states in quantum statistical mechanics

  • R. Haag
  • N. M. Hugenholtz
  • M. Winnink
Article

Abstract

Representations of theC*-algebra\(\mathfrak{A}\) of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential μ are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of\(\mathfrak{A}\) onto its commutant. This means that there is an equivalent anti-linear representation of\(\mathfrak{A}\) in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed.

Keywords

Boundary Condition Neural Network Statistical Physic Equilibrium State Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • R. Haag
    • 1
  • N. M. Hugenholtz
    • 2
  • M. Winnink
    • 2
  1. 1.Department of PhysicsUniversity of IllinoisUrbana
  2. 2.Natuurkundig LaboratoriumRijks-UniversiteitGroningen

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