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

Finite temperature quantum field theory on non compact domains and application to delta interactionsinteractions in three dimensions