Quantum electrodynamics in the null-plane causal perturbation theory

TL;DR

This paper develops a null-plane causal perturbation theory approach to quantum electrodynamics, establishing its equivalence with instant dynamics and analyzing the photon propagator with gauge invariance considerations.

Contribution

It introduces a null-plane causal perturbation framework for QED and demonstrates its equivalence to instant dynamics, including the construction of the photon propagator.

Findings

Null-plane QED is equivalent to instant dynamics for scattering processes.

The complete photon propagator is derived and shown to depend on gauge invariance.

Normalization of vacuum polarization aligns with traditional instant dynamics results.

Abstract

We study quantum electrodynamics (QED) in the light-front dynamical form by using null-plane causal perturbation theory. We establish the equivalence with instant dynamics for the scattering processes, whose normalization allows to construct the instantaneous terms of the usual null-plane QED Lagrangian density. Then we study vacuum polarization and normalize it by studying its insertions into M{\o}ller's scattering process, obtaining the complete photon's propagator, which turns to be equivalent to the one of instant dynamics only when gauge invariance is taken into account.