Quantum Electrodynamics in the Light-Front Weyl Gauge

TL;DR

This paper explores quantum electrodynamics in 3+1 dimensions using light-front Weyl gauge within discretised light-cone quantisation, deriving the physical Hamiltonian and analyzing residual gauge symmetries.

Contribution

It introduces a novel approach to quantising QED in the light-front Weyl gauge and derives the corresponding physical Hamiltonian with gauge fixing and residual symmetry analysis.

Findings

Derived the quantum commutation relations for independent variables.

Implemented gauge fixing to satisfy Gauss's law.

Identified residual gauge symmetries on the light-cone.

Abstract

We examine QED(3+1) quantised in the `front form' with finite `volume' regularisation, namely in Discretised Light-Cone Quantisation. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge $A^-=0$. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply `quantum mechanical gauge fixing' to implement Gau{\ss}' law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely displacements. On the light-cone the symmetry manifests itself quite differently.