Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

TL;DR

This paper applies Hamiltonian perturbation theory to Yang-Mills in Coulomb gauge, computing propagators, potentials, and the beta function at one-loop, aligning with covariant results.

Contribution

It introduces a Hamiltonian perturbative framework for Yang-Mills in Coulomb gauge, providing new calculations of propagators and the beta function at one-loop order.

Findings

Static gluon and ghost propagators computed at one-loop.

Static potential between color sources calculated at one-loop.

One-loop beta function matches covariant perturbation theory results.

Abstract

We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in Rayleigh-Schroedinger perturbation theory. The static gluon and ghost propagator as well as the potential between static colour sources are calculated to one-loop order. Furthermore, the one-loop $\beta$-function is calculated from both the ghost-gluon vertex and the static potential and found to agree with the result of covariant perturbation theory.