Vacuum polarization of a quantized scalar field in the thermal state in a long throat

TL;DR

This paper investigates the vacuum polarization of scalar fields in a long throat background, deriving an analytical approximation for the renormalized expectation value of the field squared, considering various masses, couplings, and temperatures.

Contribution

It provides the first analytical approximation for vacuum polarization of scalar fields in a long throat with arbitrary mass, coupling, and thermal state.

Findings

Analytical expression for <  ight>_{ren} derived.

Results applicable to both massive and massless scalar fields.

Framework accommodates arbitrary temperature and coupling to curvature.

Abstract

Vacuum polarization of scalar fields in the background of a long throat is investigated. The field is assumed to be both massive or massless, with arbitrary coupling to the scalar curvature, and in a thermal state at an arbitrary temperature. Analytical approximation for $\left< \varphi^2 \right>_{ren}$ is obtained.