Evaluating loop diagrams in a cavity (II). The vacuum polarization in scalar QED

Abstract

In a previous paper (part (I)) we have introduced a new numerical technique to evaluate divergent loop diagrams in renormalizable cavity field theories. Subsequently, we have applied this method to the linearly divergent quark self-energy of QCD in a spherical cavity. In this paper (part (II)) it is shown that the cavity regularization technique also works for the quadratically divergent photon self-energy of scalar QED in a spherical cavity. The success of this calculation depends critically on the non-trivial cancellation of non-renormalizable divergences contained in the reflection parts of the vacuum polarization diagrams.