Leading order QCD in Coulomb gauge

TL;DR

This paper reformulates Coulomb gauge QCD using a ghost-free, nonlocal action, deriving Dyson-Schwinger equations that connect to the Hamiltonian approach and heavy quark limit, providing insights into charge conservation and infrared behavior.

Contribution

It introduces a leading order truncation of Coulomb gauge QCD that links Dyson-Schwinger equations with the Hamiltonian formalism and heavy quark physics.

Findings

Derivation of Dyson-Schwinger equations from a ghost-free, nonlocal Coulomb gauge action.

Reduction to gap equations for static gluon and quark propagators.

Establishment of a connection to the heavy quark limit and charge conservation.

Abstract

Coulomb gauge QCD in the first order formalism can be written in terms of a ghost-free, nonlocal action that ensures total color charge conservation via Gauss' law. Making an Ansatz whereby the nonlocal term (the Coulomb kernel) is replaced by its expectation value, the resulting Dyson-Schwinger equations can be derived. With a leading order truncation, these equations reduce to the gap equations for the static gluon and quark propagators obtained from a quasi-particle approximation to the canonical Hamiltonian approach. Moreover a connection to the heavy quark limit can be established, allowing an intuitive explanation for the charge constraint and infrared divergences.