Canonical Quantization for the Light-Front Weyl Gauge

TL;DR

This paper develops a canonical quantization approach for Abelian gauge fields in the light-front Weyl gauge, analyzing both 1+1 and higher dimensions, and establishes the equivalence of light-front and equal-time perturbation theories.

Contribution

It introduces a systematic canonical quantization method for light-front Abelian gauge fields with Weyl gauge, including gauge fixing, physical state selection, and propagator derivation.

Findings

Derived gauge field propagators with ML prescription.

Established equivalence of light-front and equal-time perturbation theories.

Recovered Poincare covariance in the physical subspace.

Abstract

The canonical quantization on a single light front is performed for the Abelian gauge fields with the Weyl gauge coupled with fermion field currents. The analysis is carried separately for 1+1 dimensions and for higher dimensions. The Gauss law, implemented weakly as the condition on states, selects physical subspace with the Poincare covariance recovered. The perturbative gauge field propagators are found with the ML prescription for their spurious poles. The LF Feynman rules are found and their equivalence with the usual equal-time perturbation for the S-matrix elements is studied for all orders.