Revisiting the equivalence of light-front and covariant QED in the light-cone gauge

TL;DR

This paper demonstrates the equivalence between light-front time-ordered perturbation theory and covariant quantum electrodynamics in the light-cone gauge at one-loop level, clarifying the correct form of the gauge-field propagator.

Contribution

It provides a detailed proof of the equivalence between the two formulations of QED in light-front quantization, resolving previous controversies about the gauge-field propagator.

Findings

Confirmed the equivalence at one-loop level

Clarified the correct gauge-field propagator form

Connected covariant and light-front perturbation theories

Abstract

We discuss the equivalence between light-front time-ordered-perturbation theory and covariant quantum field theory in light-front quantization, in the case of quantum electrodynamics at one-loop level. In particular, we review the one-loop calculation of the vertex correction, fermion self-energy and vacuum polarization. We apply the procedure of integration by residue over the light-front energy in the loop to show how the perturbative expansion in covariant terms can be reduced to a sum of propagating and instantaneous diagrams of light-front time-ordered perturbation theory. The detailed proof of equivalence between the two formulations of the theory resolves the controversial question on which form should be used for the gauge-field propagator in the light-cone gauge in the covariant approach.