Eur. Phys. J. Plus (2022) 137: 287
https://doi.org/10.1140/epjp/s13360-022-02459-3

Regular Article

Null-plane causal perturbation theory

Institute for Theoretical Physics (IFT), São Paulo State University (UNESP), R. Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP, Brazil

^a oscar.acevedo@unesp.br

Received: 15 October 2021
Accepted: 8 February 2022
Published online: 28 February 2022

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.