Casimir Energies in the Light of Renormalizable Quantum Field Theories

Effective hadron models commonly require the computation of functional determinants. In the static case these are one–loop vacuum polarization energies, known as Casimir energies. In this talk I will present general methods to efficiently compute renormalized one–loop vacuum polarization energies and energy densities and apply these methods to construct soliton solutions within a variational approach. This calculational method is particularly useful to study singular limits that emerge in the discussion of the classical Casimir problem which is usually posed as the response of a fluctuating quantum field to externally imposed boundary conditions.