First results for the Coulomb gauge integrals using NDIM

Abstract

The Coulomb gauge has at least two advantadges over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop integrations are not well-defined (there are the so-called energy integrals) even within the context of dimensional regularization. Leibbrandt and Williams proposed a possible cure to such a problem by splitting the space-time dimension into $D=ω+ρ$, i.e., introducing a specific one parameter $ρ$ to regulate the energy integrals. The aim of our work is to apply negative dimensional integration method (NDIM) to the Coulomb gauge integrals using the recipe of split-dimension parameters and present complete results -- finite and divergent parts -- to the one and two-loop level for arbitrary exponents of propagators and dimension.