Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge

TL;DR

This paper numerically solves Dyson-Schwinger equations in Coulomb gauge, presenting a new solution that yields a linearly rising quark potential and calculating related physical quantities.

Contribution

It introduces a novel numerical solution to Dyson-Schwinger equations in Coulomb gauge with implications for quark confinement.

Findings

New solution produces a linearly rising static quark potential

Calculated the running coupling constant from the ghost-gluon vertex

Confirmed the infrared behavior observed in earlier analyses

Abstract

The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the Dyson-Schwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghost-gluon vertex.