Zero-point energy of fields in a finite volume

The zero-point energy is studied in the MIT bag model in which the quantum fields are confined, in a covariant way, to a finite region of space. The calculations are performed in the static boundary approximation. The resulting eigenfrequencies are summed using a cutoff. For the three-dimensional problem, new methods are introduced to compute the zero-point energy and to isolate the divergences occurring when the cutoff is removed. Divergences are found which cannot be absorbed by renormalizing the physical parameters in the bag model Lagrangian, as currently formulated. Alternatives are suggested and analyzed.