The Casimir effect in a solid ball when εμ = 1

Abstract

The Casimir surface force density on a solid ball is calculated assuming that the medium satisfies the relationship εμ = 1, ε being the permittivity and μ the permeability. Remarkably enough, the cutoff problems which otherwise plague calculations of the Casimir stress on dielectric nonmagnetic balls disappear, and one arrives at a cutoff independent, finite, and repulsive result for the force. When μ → 0 or μ → ∞ one finds exactly the same result as in the case of a perfectly conducting shell. Another virtue of the theory is that one may avoid the subtraction of contact terms, as the contact terms are simply vanishing. Finally, the theory is immediately applicable to a gluonic (nonquark) bag in QCD, assuming no gluonic interaction. The surface force in QCD becomes repulsive, just as in QED.