Cutoff dependence of the Casimir force within an inhomogeneous medium

Abstract

We consider the ground-state energy of the electromagnetic field in a piston geometry. In the idealized case, where the piston and the walls of the chamber are taken as perfect mirrors, the Casimir pressure on the piston is finite and independent of the small-scale physics of the media that compose the mirrors; the Casimir energy of the system can be regularized and is cutoff independent. Yet we find that, when the body of the piston is filled with an inhomogeneous dielectric medium, the Casimir energy is cutoff dependent, and the value of the pressure is thus inextricably dependent on the detailed behavior of the mirror and the medium at large wave vectors. This result is inconsistent with recent proposals for regularizing Casimir forces in inhomogeneous media.