The relation between KMS states for different temperatures

Abstract

Given a thermal field theory for some temperature β-1, we construct the theory at an arbitrary temperature 1/β′. Our work is based on a construction invented by Buchholz and Junglas, which we adapt to thermal field theories. In a first step we construct states which closely resemble KMS states for the new temperature in a local region script O sign ο ⊂ ℝ4, but coincide with the given KMS state in the space-like complement of a slightly larger region script O sign. By a weak*-compactness argument there always exists a convergent subnet of states as the size of script O signο and script O sign̂ tends towards ℝ4. Whether or not such a limit state is a global KMS state for the new temperature, depends on the surface energy contained in the layer in between the boundaries of script O signο and script O sign̂. We show that this surface energy can be controlled by a generalized cluster condition.