Fictitious Cavity Approach to the Casimir Effect

TL;DR

This paper introduces a versatile method for calculating Casimir energy and force in cavities with arbitrary materials, generalizing the Lifshitz formula to various geometries.

Contribution

It presents a new, adaptable approach for Casimir effect calculations applicable to diverse cavity shapes and materials, extending existing formulas.

Findings

Derived general expressions for Casimir energy and force.

Reproduced the Lifshitz formula for planar cavities.

Demonstrated the approach's applicability to other geometries.

Abstract

We obtain expressions for the Casimir energy and force following an approach which may be applied to cavities made up of arbitrary materials. In the case of planar cavities we obtain the well known Lifshitz formula. The approach is easily generalizable to other geometries.