On the Discretized Light-Cone Quantization of Electrodynamics

TL;DR

This paper explores the discretized light-cone quantization of (3+1)-dimensional electrodynamics, focusing on gauge fixing, zero modes, and their impact on the fermion self-energy, providing a framework for nonperturbative analysis.

Contribution

It introduces a natural gauge choice for zero modes and solves the constraints perturbatively, advancing the understanding of light-cone quantization in electrodynamics.

Findings

Identified a gauge where zero modes satisfy canonical commutation relations.

Constructed Poincaré generators in the discretized framework.

Analyzed the impact of zero modes on the one-loop fermion self-energy.

Abstract

Discretized light-cone quantization of (3+1)-dimensional electrodynamics is discussed, with careful attention paid to the interplay between gauge choice and boundary conditions. In the zero longitudinal momentum sector of the theory a general gauge fixing is performed, and the corresponding relations that determine the zero modes of the gauge field are obtained. One particularly natural gauge choice in the zero mode sector is identified, for which the constraint relations are simplest and the fields may be taken to satisfy the usual canonical commutation relations. The constraints are solved in perturbation theory, and the Poincar\'e generators $P^\mu$ are constructed. The effect of the zero mode contributions on the one-loop fermion self-energy is studied.