The Coulomb gauge ghost Dyson-Schwinger equation

TL;DR

This paper numerically investigates the ghost Dyson-Schwinger equation in Coulomb gauge, revealing how boundary conditions influence solutions and their relation to confinement mechanisms.

Contribution

It introduces a nonperturbative boundary condition to fully solve the ghost Dyson-Schwinger equation and links solution patterns to Gribov ambiguity and confinement.

Findings

Solutions follow a critical pattern at high momenta

Infrared solutions depend on boundary conditions

Renormalization is largely boundary-condition independent

Abstract

A numerical study of the ghost Dyson-Schwinger equation in Coulomb gauge is performed and solutions for the ghost propagator found. As input, lattice results for the spatial gluon propagator are used. It is shown that in order to solve completely, the equation must be supplemented by a nonperturbative boundary condition (the value of the inverse ghost propagator dressing function at zero momentum) which determines if the solution is critical (zero value for the boundary condition) or subcritical (finite value). The various solutions exhibit a characteristic behavior where all curves follow the same (critical) solution when going from high to low momenta until `forced' to freeze out in the infrared to the value of the boundary condition. The renormalization is shown to be largely independent of the boundary condition. The boundary condition and the pattern of the solutions can be interpreted in terms of the Gribov gauge-fixing ambiguity. The connection to the temporal gluon propagator and the infrared slavery picture of confinement is explored.