Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism

TL;DR

This paper develops a perturbative approach to Coulomb gauge Yang-Mills theory using first order formalism, deriving analytic expressions for two-point functions at one-loop order, highlighting their finiteness properties and singularity structure.

Contribution

It introduces a differential equation technique and dimensional regularization to analytically compute one-loop two-point functions in Coulomb gauge Yang-Mills theory within the first order formalism.

Findings

Ultraviolet divergent parts are explicitly derived.

Finite parts are finite at spacelike momenta.

Results reveal light-cone singularities and branch cuts.

Abstract

Perturbative Coulomb gauge Yang-Mills theory within the first order formalism is considered. Using a differential equation technique and dimensional regularization, analytic results for both the ultraviolet divergent and finite parts of the two-point functions at one-loop order are derived. It is shown how the non-ultraviolet divergent parts of the results are finite at spacelike momenta with kinematical singularities on the light-cone and subsequent branch cuts extending into the timelike region.