Null-plane causal perturbation theory

Abstract

We reconstruct causal perturbation theory in a way compatible with light-front dynamics on the basis of Rohrlich’s invariant null-plane coordinatization. We show that, when the causality axiom is referred to the x+ time coordinate, the retarded and advanced distributions are possibly non-null on the entire x--axis, despite which Bogoliubov–Medvedev–Polivanov’s axioms still have a perturbative solution whose practical implementation is exposed in detail. Our results are then applied to the construction of the free fields Feynman’s propagators, for which instantaneous terms arise in the fermion and massless vector cases, and then to Yukawa’s model for the interaction of a neutral pseudo-scalar field with nucleons.