Some differences between Dirac's hole theory and quantum field theory

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered equivalent. However, it was recently shown by several investigators that this is not necessarily the case because when the change in the vacuum energy was calculated for a time-independent perturbation, HT and QFT yielded different results. In this paper, we extend this discussion to include a time-dependent perturbation for which the exact solution to the Dirac equation is known. We show that for this case also, HT and QFT yield different results. In addition, we offer some discussion of the problem of anomalies in QFT.