Constraints imposed upon a state of a system that satisfies the K.M.S. boundary condition

It is shown that K.M.S.-states are locally normal on a great number of C*-algebras that may be of interest in Quantum Statistical Mechanics. The lattice structure and the Choquet-simplex structure of various sets of states are investigated. In this respect special attention is payed to the interplay of the K.M.S.-automorphism group with other automorphism groups under whose action K.M.S.-states are possibly invariant. A seemingly weaker notion than G-abelianness of the algebra of observables, namely G'abelianness, is introduced and investigated. Finally a necessary and sufficient condition (on a C*-algebra with a sequential separable factor funnel) for decomposition of a locally normal state into locally normal states is given.

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“…(The latter fact in the case of a simple algebra implies that τ g commutes with the K.M.S. automorphisms [32]. )…”

Section: Furthermore the Abelian Von Neumann Algebra [π ω (U)ul^ω )mentioning

confidence: 98%

“…Since ω is a faithful state on lί we have then [32,37] that This equation implies that l7 f F_ f e £( §)' = {λl}, i.e. [7 f K_ t = expiα(ί) where ί->α(ί) is a real function on the real line.…”

Section: (σ T (A) B) and F(t + Iβ) = ω(Bσ T (A)\~]mentioning

confidence: 99%

Local normality in Quantum Statistical Mechanics

Takesaki

Winnink

1973

Commun.Math. Phys.

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“…Remark The above proof simplifies the original theorem in [SW70]. The above approach identifies what seems to be a central element in the issue equilibrium vs non-equilibrium in the present context: the same state and two different dynamics under which the state is assumed invariant (note that KMS states are necessarily invariant if the dynamics are implemented by an automorphism).…”

Section: A General Approach To Non-equilibrium States: the Sirugue-wimentioning

confidence: 84%