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Communications in Mathematical Physics

, Volume 70, Issue 3, pp 193–212 | Cite as

Group duality and the Kubo-Martin-Schwinger condition

  • D. Kastler
  • M. Takesaki
Article

Abstract

We consider clusteringG-invariant states of aC*-algebraU endowed with an action of a locally compact abelian groupG. Denoting as usual byFAB,GAB, the corresponding two-point functions, we give criteria for the fulfillment of the KMS condition (w.r.t. some one-parameter subgroup ofG) based upon the existence of a closable mapT such thatTFAB =GAB for allA,BU. Closability is either inL(G),B(G), orC(G), according to clustering assumptions. Our criteria originate from the combination of duality results for the groupG (phrased in terms of functions systems), with density results for the two-point functions.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics allA 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • D. Kastler
    • 2
    • 1
  • M. Takesaki
    • 3
    • 1
  1. 1.Centre de Physique Théorique du CNRS II, Marseille-LuminyMarseilleFrance
  2. 2.Département de PhysiqueUER Scientifique de Marseille-LuminyMarseilleFrance
  3. 3.Département de MathématiquesUER Scientifique de Marseille-LuminyMarseilleFrance

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