Equivalence of renormalized covariant and light-front perturbation theory. I. Longitudinal divergences in the Yukawa model

Light-front perturbation theory (LFPT) has been proposed as an alternative to covariant perturbation theory. LFPT is only acceptable if it produces invariant S-matrix elements. Doubts have been raised concerning the equivalence of LFPT and covariant perturbation theory. The main obstacles to a rigorous proof of equivalence are algebraic complexity in the case of arbitrarily high orders in perturbation theory and the occurrence of longitudinal divergences not present in covariant perturbation theory. We show in the case of the Yukawa model of fermions interacting with scalar bosons at the one-loop level how to deal with the longitudinal divergences. Invariant S-matrix elements are obtained using our method.