Dynamical Zero Modes and Pure Glue ${\bf{\rm{QCD}}_{1+1}}$ in Light-Cone Field Theory

TL;DR

This paper investigates the structure of pure glue ${ m{QCD}}_{1+1}$ in light-cone quantization, revealing the role of dynamical zero modes, gauge ambiguities, and the spectrum of vacuum states.

Contribution

It provides an exact solution for pure glue theory with zero modes in light-cone quantization, clarifying gauge issues and vacuum structure.

Findings

Discovered a discrete spectrum of vacuum states.

Identified the gauge invariance of zero modes.

Verified the equivalence of front and instant form approaches.

Abstract

We consider light-cone quantized ${\rm{QCD}}_{1+1}$ on a `cylinder' with periodic boundary conditions on the gluon fields. This is the framework of discretized light-cone quantization. We review the argument that the light-cone gauge $A^+=0$ is not attainable. The zero mode is a dynamical and gauge invariant field. The attainable gauge has a Gribov ambiguity. We exactly solve the problem of pure glue theory coupled to some zero mode external sources. We verify the identity of the front and the more familiar instant form approaches. We obtain a discrete spectrum of vacuum states and their wavefunctions.