Quantum Mechanics of Dynamical Zero Mode in $QCD_{1+1}$ on the Light-Cone

TL;DR

This paper explores the dynamical zero mode in light-cone quantized QCD in 1+1 dimensions on a circle, revealing its nontrivial role in the vacuum structure and constructing the ground state within a specific approximation.

Contribution

It demonstrates that the zero mode is a dynamical field affecting the vacuum, and constructs the ground state of the system in a particular approximation.

Findings

Zero mode is dynamical and influences vacuum structure.

Constructed the ground state of the system.

Compared results with previous work in a specific coupling region.

Abstract

Motivated by the work of Kalloniatis, Pauli and Pinsky, we consider the theory of light-cone quantized $QCD_{1+1}$ on a spatial circle with periodic and anti-periodic boundary conditions on the gluon and quark fields respectively. This approach is based on Discretized Light-Cone Quantization (DLCQ). We investigate the canonical structures of the theory. We show that the traditional light-cone gauge $A_- = 0$ is not available and the zero mode (ZM) is a dynamical field, which might contribute to the vacuum structure nontrivially. We construct the full ground state of the system and obtain the Schr\"{o}dinger equation for ZM in a certain approximation. The results obtained here are compared to those of Kalloniatis et al. in a specific coupling region.