Casimir Energy Corrections by Light-Cone Fluctuations

TL;DR

This paper investigates how light-cone fluctuations, modeled as space-time dependent randomness, modify the Casimir energy between parallel plates, leading to a correction that scales as 1/a^8 and affects vacuum pressure uniformity.

Contribution

It introduces a novel approach to simulate light-cone fluctuations using a random coefficient in the Klein-Gordon operator and analyzes their impact on Casimir energy corrections.

Findings

Correction to vacuum energy density scales as 1/a^8

Light-cone fluctuations break vacuum pressure homogeneity

Standard Casimir energy dependence of 1/a^4 is modified

Abstract

We study the effects of light-cone fluctuations on the renormalized zero-point energy associated with a free massless scalar field in the presence of boundaries. In order to simulate light-cone fluctuations we introduce a space-time dependent random coefficient in the Klein-Gordon operator. We assume that the field is defined in a domain with one confined direction. For simplicity, we choose the symmetric case of two parallel plates separated by a distance $a$. The correction to the renormalized vacuum energy density between the plates goes as $1/a^{8}$ instead of the usual $1/a^{4}$ dependence for the free case. In turn we also show that light-cone fluctuations break down the vacuum pressure homogeneity between the plates.