Reconsidering the Vacuum Energy of a Massive Scalar Field in a Spherical Cavity

Abstract

We reconsider the vacuum (Casimir) energy of a massive scalar field obeying Dirichlet boundary conditions inside a spherical cavity. Using zeta-function regularization, we carefully recalculate the analytic part of the zeta function via the uniform asymptotic expansion of the modified Bessel functions. We correct a sign error present in an earlier calculation (PR D56 (1997) 4896) that affected the large-mass behavior. The renormalized vacuum energy is shown to vanish for large mass, as required on physical grounds. Numerical results reveal that the energy changes sign several times as a function of the cavity radius.