The perfect magnetic conductor (PMC) Casimir piston in d+1 dimensions

TL;DR

This paper analyzes the Casimir effect for perfect magnetic conductor (PMC) boundaries in various dimensions, deriving exact force expressions and revealing that the force is attractive, with implications for future experiments and related PEC studies.

Contribution

The study provides explicit formulas for PMC Casimir energies and forces in d+1 dimensions, including new expressions for PEC pistons and force calculations in specific geometries.

Findings

Casimir force for PMC is attractive in all examined dimensions

Derived exact d-dimensional expressions for Casimir force on the piston

Provided alternative formulas for PEC Casimir piston in 3+1 dimensions

Abstract

Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC's and Casimir experiments involving structures that approximate PMC's may be carried out in the not too distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in $d+1$ dimensions. The PMC Casimir energy is explicitly evaluated by summing over $p+1$-dimensional Dirichlet energies where p ranges from 2 to $d$ inclusively. We derive two exact $d$-dimensional expressions for the Casimir force on the piston and find that the force is negative (attractive) in all dimensions. Both expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from our work is a contribution to the PEC literature: we obtain a useful alternative expression for the PEC Casimir piston in 3+1 dimensions and also evaluate the Casimir force per unit area on an infinite strip, a geometry of experimental interest.