Consistent perturbative light-front formulation of quantum electrodynamics

TL;DR

This paper develops a consistent light-front formulation of quantum electrodynamics (QED) using standard perturbation theory, ensuring correct treatment of singularities and agreement with traditional calculations.

Contribution

It introduces a new light-front QED formulation with a specific gauge choice that reproduces the Mandelstam-Leibbrandt prescription and matches standard off-shell amplitudes.

Findings

Reproduces Mandelstam-Leibbrandt causal prescription.

Matches standard off-shell amplitude calculations.

Provides a consistent perturbative framework for light-front QED.

Abstract

A new light-front formulation of Q.E.D. is developed, within the framework of standard perturbation theory, in which $x^+$ plays the role of the evolution parameter and the gauge choice is $A_+=0$ (light-front "temporal" gauge). It is shown that this formulation leads to the Mandelstam-Leibbrandt causal prescription for the non-covariant singularities in the photon propagator. Furthermore, it is proved that the dimensionally regularized one loop off-shell amplitudes exactly coincide with the correct ones, as computed within the standard approach using ordinary space-time coordinates.