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 $Ø_\circ \subset \rr^4$, but coincide with the given KMS state in the space-like complement of a slightly larger region $\hatØ$. By a weak*-compactness argument there always exists a convergent subnet of states as the size of $ Ø_\circ$ and $ \hatØ$ tends towards $ \rr^4$. 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 $ Ø_\circ$ and $ \hatØ$. We show that this surface energy can be controlled by a generalized cluster condition.