Casimir energies for massive scalar fields in a spherical geometry

The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical surface is obtained. The field is considered, separately, inside and outside the surface. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular, the differences occurring with respect to the case when the field occupies the whole space. The final result contains several constants that experience renormalization and can be determined only experimentally. The nontrivial finite parts that appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time. [S0556-2821(97)04220-3]. PACS number(s): 04.62.+v, 12.39.Hg.