Finiteness of the Coulomb gauge QCD perturbative effective action

TL;DR

This paper proves that energy divergences in individual Feynman graphs at 2-loop order in Coulomb gauge cancel out in combinations, generalizing the Christ-Lee term for the effective action.

Contribution

It demonstrates the cancellation of energy divergences at 2-loop order in Coulomb gauge and extends the Christ-Lee term to the effective action.

Findings

Energy divergences cancel in combined graphs at 2-loop order

Generalization of the Christ-Lee term for the effective action

Validation of divergence cancellation beyond transverse external fields

Abstract

At 2-loop order in the Coulomb gauge, individual Feynman graphs contributing to the effective action have energy divergences. It is proved that these cancel in suitable combinations of graphs. This has previously been shown only for transverse external fields. The calculation results in a generalization of the Christ-Lee term which was inserted into the Hamiltonian.