Cancellation of energy-divergences in Coulomb gauge QCD

TL;DR

This paper investigates energy-divergences in Coulomb gauge QCD, demonstrating their cancellation at two-loop order through Ward identities, thus clarifying the consistency of the Hamiltonian formulation.

Contribution

It shows how energy-divergences in Coulomb gauge QCD cancel at two-loop order using Ward identities, resolving a key issue in the Hamiltonian formulation.

Findings

Energy-divergences are present in individual graphs.

These divergences cancel out at 2-loop order.

Ward identities ensure the cancellation of divergences.

Abstract

In the Coulomb gauge of nonabelian gauge theories there are in general, in individual graphs, 'energy-divergences' on integrating over the loop energy variable for fixed loop momentum. These divergences are avoided in the Hamiltonian, phase-space formulation. But, even in this formulation, energy-divergences re-appear at 2-loop order. We show in an example how these cancel between graphs as a consequence of Ward identities.