Dependence of the vacuum energy on spherically symmetric background fields

TL;DR

This paper investigates how the vacuum energy of a scalar field varies in spherically symmetric backgrounds, emphasizing the influence of potentials and bound states through refined numerical methods.

Contribution

It refines numerical techniques from prior work and demonstrates the impact of repulsive potentials and bound states on vacuum energy in spherical backgrounds.

Findings

Repulsive potentials contribute positively to vacuum energy.

Bound states play a crucial role in vacuum energy calculations.

Numerical evidence supports the influence of background fields on vacuum energy.

Abstract

The vacuum energy of a scalar field in a spherically symmetric background field is considered. Based on previous work [hep-th/9608070], the numerical procedure is refined further and applied to several examples. We provide numerical evidence that repulsive potentials lead to positive contributions to the vacuum energy. Furthermore, the crucial role played by bound-states is clearly seen.