RADIATIVE CORRECTION TO THE CASIMIR FORCE ON A SPHERE - ART. NO. 045003

The first radiative correction to the Casimir energy of a perfectly co nducting spherical shell is calculated. The calculation is performed i n the framework of covariant perturbation theory with the boundary con ditions implemented as constraints. The formalism is briefly reviewed and its use is explained by deriving the known results for two paralle l planes. The ultraviolet divergencies are shown to have the same stru cture as those for a massive field in zeroth order of alpha. In the ze ta-functional regularization employed by us no divergencies appear. If the radius of the sphere is large compared to the Compton wavelength of the electron the radiative correction is of order alpha/(R(2)m(e)) and contains a logarithmic dependence on m(e)R. It has the opposite si gn but the same order of magnitude as in the case of two parallel plan es. [S0556-2821(98)04914-5].