The Equal-Time Quark Propagator in Coulomb Gauge

TL;DR

This paper studies the equal-time quark propagator in Coulomb gauge using a Hamiltonian approach, revealing that its infrared behavior is mainly influenced by the Coulomb potential, with minimal impact from spatial gluon coupling.

Contribution

It introduces a non-Gaussian vacuum wave functional and solves the Dyson-Schwinger equations for the quark propagator in Coulomb gauge, highlighting the dominance of the Coulomb potential.

Findings

Quark propagator is insensitive to spatial gluon coupling.

Infrared behavior is governed by the Coulomb potential.

Approximation used simplifies the understanding of quark confinement.

Abstract

We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD. We use a non-Gaussian vacuum wave functional which includes the coupling of the quarks to the spatial gluons. The expectation value of the QCD Hamiltonian is expressed by the variational kernels of the vacuum wave functional by using the canonical recursive Dyson--Schwinger equations (CRDSEs) derived previously. Assuming the Gribov formula for the gluon energy we solve the CRDSE for the quark propagator in the bare-vertex approximation together with the variational equations of the quark sector. Within our approximation the quark propagator is fairly insensitive to the coupling to the spatial gluons and its infrared behaviour is exclusively determined by the strongly infrared diverging instantaneous colour Coulomb potential.