Abstract
A strongly continuous one parameter group of *-automorphisms of aC*-algebra with unit is said to be approximately inner if it can be approximated strongly by inner one parameter groups of *-automorphisms. It is shown that an approximately inner one parameter group of *-automorphisms has a ground state and, if there exists a trace state, a KMS state for all inverse temperatures. It follows that quantum lattice systems have ground states and KMS states. Conditions that a strongly continuous one parameter group of *-automorphisms of a UHF algebra be approximately inner are given in terms of the unbounded derivation which generates the automorphism group.
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Communicated by A. S. Wightman
This research is supported in part by a National Science Foundation Grant.
Alfred P. Sloan Fellow.
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Powers, R.T., Sakai, S. Existence of ground states and KMS states for approximately inner dynamics. Commun.Math. Phys. 39, 273–288 (1975). https://doi.org/10.1007/BF01705375
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DOI: https://doi.org/10.1007/BF01705375