Local $\zeta$-functions, stress-energy tensor, field fluctuations, and all that, in curved static spacetime

TL;DR

This paper reviews the application of local zeta functions in quantum field theory on curved static spacetimes, focusing on regularizing the stress-energy tensor and field fluctuations.

Contribution

It provides an overview of the techniques involving local zeta functions for regularization in quantum field theory in curved static spacetimes.

Findings

Effective regularization of stress-energy tensor

Calculation of field fluctuations in curved spacetime

Summary of local zeta function methods

Abstract

This is a quick review on some technology concerning the local zeta function applied to Quantum Field Theory in curved static (thermal) spacetime to regularize the stress-energy tensor and the field fluctuations.