Calculation of the regularized vacuum energy in cavity field theories

A novel technique based on Schwinger's proper time method is applied to the Casimir problem of the M.I.T. bag model. Calculations of the regularized v acuum energies of massless scalar and Dirac spinor fields confined to a sta tic and spherical cavity are presented in a consistent manner. While our re sults agree partly with previous calculations based on asymptotic methods:, the main advantage of our technique is that the numerical errors;ire under control. Interpreting the bag constant as a vacuum expectation value, we i nvestigate potential cancellations of boundary divergences between the cano nical energy and its bag constant counterpart in tie fermionic case. It is found that:such cancellations do not occur.