Detlev Buchholz, Christian D. Jaekel
The Relation between KMS--States for Different Temperatures
Preprint series: ESI preprints

MSC:

81T05 Axiomatic quantum field theory; operator algebras

Abstract: Some years ago Buchholz and Junglas [BJu 89]
established the existence of thermal equilibrium states
(KMS-states) for a large class of quantum field theories.
The KMS-states were constructed as limit points of states
which represent strictly localized excitations of
the vacuum. We adjust their method such that it
respects the general structure of thermal quantum field
theory [J\"a b]. In a first step we construct states which
look like KMS-states for a new temperature in a
local region $\scriptstyle \O_\circ \subset \r^4$ but
coincide with the given KMS-state in the spatial complement
of a slightly larger region $\scriptstyle \hat{\O}$.
The existence of limit points of these nets of states,
which are global KMS-states for the new temperature,
depends crucially on the surface energy contained
in the layer in between the boundaries of
$\scriptstyle \O_\circ$ and $\scriptstyle \hat{\O}$.
Introducing an auxiliary structure and applying a
generalized cluster theorem, we can controll the surface
effects in all thermal theories with a physically sensible
number of local degrees of freedom.~I.e.,
given a thermal field theory that corresponds to a certain
temperature, our method shows that it is possible to
construct the theory at any positive, finite temperature
provided the number of local degrees of freedom is
restricted in a physically sensible manner.
Keywords: algebraic quantum field theory, KMS-state, thermal quantum field theory