Light-cone fluctuations and the renormalized stress tensor of a massless scalar field

TL;DR

This paper examines how light-cone fluctuations, modeled as a random Klein-Gordon equation, affect the vacuum expectation value of the stress-energy tensor for a massless scalar field in a flat spacetime with nontrivial topology.

Contribution

It introduces a model for light-cone fluctuations using a random Klein-Gordon equation and computes the averaged correction to the stress-energy tensor in a ($d+1$)-dimensional flat space.

Findings

Derived the correction to the stress-energy tensor due to light-cone fluctuations.

Provided an explicit expression for the averaged renormalized vacuum expectation value.

Analyzed the impact of Gaussian random processes on quantum field fluctuations.

Abstract

We investigate the effects of light-cone fluctuations over the renormalized vacuum expectation value of the stress-energy tensor of a real massless minimally coupled scalar field defined in a ($d+1$)-dimensional flat space-time with topology ${\cal R}\times {\cal S}^d$. For modeling the influence of light-cone fluctuations over the quantum field, we consider a random Klein-Gordon equation. We study the case of centered Gaussian processes. After taking into account all the realizations of the random processes, we present the correction caused by random fluctuations. The averaged renormalized vacuum expectation value of the stress-energy associated with the scalar field is presented.