VACUUM ENERGY IN SPHERICAL DOMAINS - WKB AND UNIFORM ASYMPTOTIC EXPANSIONS

We evaluate the finite part of the regularized zero-point energy for a massless scalar field confined in the interior of a D-dimensional sph erical region. While some insight is offered into the dimensional depe ndence of the WKB approximations by examining the residues of the spec tral-zeta-function poles, a mode-sum technique based on an integral re presentation of the Bessel spectral zeta function is applied with the help of uniform asymptotic expansions (u.a.e.'s).