Casimir Effect in the Presence of External Fields

TL;DR

This paper investigates the Casimir effect for scalar fields with boundaries and external potentials, providing analytic and numerical results for piston configurations, including higher-dimensional generalizations with Kaluza-Klein dimensions.

Contribution

It introduces a novel approach to analyze the Casimir effect in the presence of arbitrary smooth potentials and extends the analysis to higher dimensions with explicit numerical results.

Findings

Analytic expressions for Casimir energy and force in piston configurations.

Numerical results for compactly supported potentials modeled as delta-sequences.

Generalization of results to higher-dimensional pistons with Kaluza-Klein dimensions.

Abstract

In this work the Casimir effect is studied for scalar fields in the presence of boundaries and under the influence of arbitrary smooth potentials of compact support. In this setting, piston configurations are analyzed in which the piston is modeled by a potential. For these configurations, analytic results for the Casimir energy and force are obtained by employing the zeta function regularization method. Also, explicit numerical results for the Casimir force are provided for pistons modeled by a class of compactly supported potentials that are realizable as delta-sequences. These results are then generalized to higher dimensional pistons by considering additional Kaluza-Klein dimensions.