Canonical Formulation of the Light-Front Gluodynamics and Quantization of the Non-Abelian Plane Waves

TL;DR

This paper develops a gauge-invariant canonical formulation of light-front SU(2) gluodynamics, deriving a quantized spectrum of classical non-Abelian plane waves and exploring phase dependence in the infinite volume limit.

Contribution

It introduces a gauge-invariant canonical framework for light-front gluodynamics and quantizes non-Abelian plane waves without gauge fixing.

Findings

Discrete spectrum of light-front Hamiltonian at finite volume

Mass gap depends on the infinite volume limit procedure

Formulation aligns with covariant gauge perturbation theory

Abstract

Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.