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

TL;DR

This paper extends the zeta function approach to finite temperature quantum field theory on non-compact spaces and applies it to Schrödinger operators with delta potentials in three dimensions.

Contribution

It introduces a method to handle non-compact spatial sections in quantum field theory using relative zeta functions, expanding the scope of existing techniques.

Findings

Extended the decomposition of the zeta regularized partition function to non-compact spaces.

Applied the method to Schrödinger operators with delta-like potentials in three dimensions.

Provided a framework for analyzing quantum fields with singular interactions.

Abstract

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}.