Communications in Mathematical Physics

, Volume 5, Issue 3, pp 215–236

On the equilibrium states in quantum statistical mechanics

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

DOI: 10.1007/BF01646342

Cite this article as:
Haag, R., Hugenholtz, N.M. & Winnink, M. Commun.Math. Phys. (1967) 5: 215. doi:10.1007/BF01646342

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.

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
  3. 3.II. Institut für theoretische Physik2 Hamburg 50Germany

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