The ghost propagator in Coulomb gauge

TL;DR

This paper investigates the ghost propagator in Coulomb gauge using lattice data and Dyson-Schwinger equations, revealing how boundary conditions influence solutions and their relation to confinement.

Contribution

It introduces a boundary condition approach to solving the ghost Dyson-Schwinger equation in Coulomb gauge, clarifying the role of Gribov ambiguity and infrared behavior.

Findings

Critical and subcritical solutions depend on boundary conditions.

Infrared behavior shows solutions freeze out at boundary values.

Connection established between ghost propagator, confinement, and Gribov ambiguity.

Abstract

We present results for a numerical study of the ghost propagator in Coulomb gauge whereby lattice results for the spatial gluon propagator are used as input to solving the ghost Dyson-Schwinger equation. We show that in order to solve completely, the ghost equation must be supplemented by a 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 boundary condition can be interpreted in terms of the Gribov gauge-fixing ambiguity; we also demonstrate that this is not connected to the renormalization. Further, the connection to the temporal gluon propagator and the infrared slavery picture of confinement is discussed.