Dirac's hole theory versus field theory for a time dependent perturbation

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered to be equivalent to each other. However, it has been recently shown that for a time independent perturbation different results are obtained when the change in the vacuum energy is calculated. Here we shall extend this discussion to include a time dependent perturbation. It will be shown that HT and QFT yield different results for the change in the vacuum energy due to a time dependent perturbation.