Light-Front-Quantized QCD in Covariant Gauge

TL;DR

This paper develops a covariant gauge light-front quantization of QCD, demonstrating causal propagators and rotational invariance, and illustrates the approach with QED calculations to show consistency with conventional formulations.

Contribution

It introduces a covariant gauge light-front quantization method for QCD that maintains causality and rotational invariance, addressing issues in previous light-cone gauge approaches.

Findings

Causal propagators without instantaneous terms in LF quantized theory.

Recovery of rotational invariance and Coulomb potential in covariant gauge.

Equivalence of LF quantization with conventional covariant formulations demonstrated in QED.

Abstract

The light-front (LF) canonical quantization of quantum chromodynamics in covariant gauge is discussed. The Dirac procedure is used to eliminate the constraints in the gauge-fixed front form theory quantum action and to construct the LF Hamiltonian formulation. The physical degrees of freedom emerge naturally. The propagator of the dynamical $\psi_+$ part of the free fermionic propagator in the LF quantized field theory is shown to be causal and not to contain instantaneous terms. Since the relevant propagators in the covariant gauge formulation are causal, rotational invariance---including the Coulomb potential in the static limit---can be recovered, avoiding the difficulties encountered in light-cone gauge. The Wick rotation may also be performed allowing the conversion of momentum space integrals into Euclidean space forms. Some explicit computations are done in quantum electrodynamics to illustrate the equivalence of front form theory with the conventional covariant formulation. LF quantization thus provides a consistent formulation of gauge theory, despite the fact that the hyperplanes $x^{\pm}=0$ used to impose boundary conditions constitute characteristic surfaces of a hyperbolic partial differential equation.