Canonical quantization of fields with higher-derivative couplings

It is shown with the use of a model of scalar fields how canonical quantization can carried out when the free part of the Lagrangian density involves only the first derivatives, while the coupling terms involve higher derivatives. Cancellation of noncovariant terms in the scattering operator is found to occur for such couplings provided that $\delta \mathrm{}\left(0\right)\mathrm{}$ terms are eliminated with the use of dimensional regularization.