Casimir effect for perfect electromagnetic conductors (PEMCs): A sum rule for attractive/repulsive forces

TL;DR

This paper derives a universal analytical expression for the Casimir force between perfect electromagnetic conductor plates, revealing conditions for attraction and repulsion based on duality symmetry and PEMC parameters.

Contribution

It introduces a sum rule for Casimir forces involving PEMCs, connecting attractive and repulsive regimes through a duality transformation in macroscopic quantum electrodynamics.

Findings

Derived a universal formula for Casimir force between PEMC plates.

Connected attractive and repulsive Casimir forces via duality symmetry.

Provided insights into boundary conditions affecting electromagnetic forces.

Abstract

We discuss the Casimir effect for boundary conditions involving perfect electromagnetic conductors (PEMCs). Based on the corresponding reciprocal Green's tensor we construct the Green's tensor for two perfectly reflecting plates with magnetoelectric coupling (non-reciprocal media) within the framework of macroscopic quantum electrodynamics. We calculate the Casimir force between two PEMC plates in terms of the PEMC parameter M and the duality transformation angle ${\theta}$ resulting in a universal analytic expression that connects the attractive Casimir force with the repulsive Boyer force. We relate the results to the duality symmetry of electromagnetism.