# Casimir forces in inhomogeneous media: renormalization and the principle of virtual work

## TL;DR

This paper develops a renormalization method to accurately compute Casimir forces in inhomogeneous, dispersive dielectric media, ensuring finite results and consistency with the principle of virtual work.

## Contribution

It introduces a novel renormalization scheme for Casimir forces in inhomogeneous media, extending existing theories to more complex dielectric configurations.

## Key findings

- The method yields finite, consistent Casimir force calculations.
- It extends the Dzyaloshinskii-Lifshitz-Pitaevskii force to inhomogeneous media.
- Examples demonstrate the scheme's effectiveness.

## Abstract

We calculate the Casimir forces in two configurations, namely, three parallel dielectric slabs and a dielectric slab between two perfectly conducting plates, where the dielectric materials are dispersive and inhomogeneous in the direction perpendicular to the interfaces. A renormalization scheme is proposed consisting of subtracting the effect of one interface with a single inhomogeneous medium. Some examples are worked out to illustrate this scheme. Our method always gives finite results and is consistent with the principle of virtual work; it extends the Dzyaloshinskii-Lifshitz-Pitaeveskii force to inhomogeneous media.