CASIMIR SURFACE FARCES ON DIELECTRIC MEDIA IN SPHERICAL GEOMETRY

This paper contains a calculation of the Casimir surface force density in spherical geometry under three different circumstances: (i) The system is an infinitely thin, perfectly conducting shell, endowed with dispersive properties. The presence of dispersion means that the earlier expressions calculated by Boyer (1968) and others have to be generalized; in particular, it is possible to revisit the old semiclassical electron idea of Casimir (1956). (ii) The system consists of two different spherical shells, of the same type as above. In particular, the nondispersive Casimir surface force between two flat plates is recovered as the leading term in the formalism when the curvatures of the shells go to zero. (iii) The system is a compact dielectric ball, surrounded by a vacuum. General formulae are given in all three cases, consistency checks carried out, and some simplifying approximations are given. All physical expressions, if necessary regularized by the Riemann zeta function method, are clear-cut and finite.