  We use relative zeta functions technique of W. Muller \cite{Mul} to extend
the classical decomposition of the zeta regularized partition function of a
finite temperature quantum field theory on a ultrastatic space-time with
compact spatial section to the case of non compact spatial section. As an
application, we study the case of Schr\"odinger operators with delta like
potential, as described by Albeverio & alt. in \cite{AGHH}.
