Canonical formulation of light-front gluodynamics and quantization of non-Abelian plane waves

Abstract

Without gauge fixing, canonical variables for the light-front $\mathrm{SU}(2)$ 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. Abelianization 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 ${P}_{\ensuremath{-}}.$ 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.