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

Light-front dynamics can only become a viable alternative to the covariant approach if doubts about its covariance can be taken away. As a minimal requirement we take that the physical quantities calculated with light-front perturbation theory are the same as those obtained using covariant perturbation theory. If this situation occurs, we use the word equivalent to characterize it. For quantities that involve the calculation of superficially convergent diagrams, proofs of equivalence exist. For some types of divergent diagrams the proof of equivalence is complicated. Here we deal with diagrams with transverse divergences. Our method is based on minus regularization, which is inspired on BPHZ regularization. In a calculation using numerical methods we show how to obtain a rotationally invariant amplitude for two triangle diagrams contributing to the decay of a scalar boson in the Yukawa model. It concludes our proof of equivalence of covariant and light-front perturbation theory.