Feynman rules for Coulomb gauge QCD

TL;DR

This paper develops a method to perform renormalization in Coulomb gauge QCD by re-expressing complex Christ-Lee terms as pseudo-Feynman integrals, addressing technical challenges in perturbation theory.

Contribution

It introduces a novel approach to handle Christ-Lee terms in Coulomb gauge QCD, enabling consistent renormalization despite their non-subgraph structure.

Findings

Successfully re-expressed CL terms as pseudo-Feynman integrals.

Demonstrated cancellation of energy divergences.

Provided a framework for renormalization in Coulomb gauge QCD.

Abstract

The Coulomb gauge in nonabelian gauge theories is attractive in principle, but beset with technical difficulties in perturbation theory. In addition to ordinary Feynman integrals, there are, at 2-loop order, Christ-Lee (CL) terms, derived either by correctly ordering the operators in the Hamiltonian, or by resolving ambiguous Feynman integrals. Renormalization theory depends on the subgraph structure of ordinary Feynamn graphs. The CL terms do not have subgraph structure. We show how to carry out enormalization in the presene of CL terms, by re-expressing these as `pseudo-Feynman' inegrals. We also explain how energy divergences cancel.