Split dimensional regularization for the Coulomb gauge Original Research Article

A new procedure for regularizing Feynman integrals in the non-covariant Coulomb gauge ∇ · Aa = 0 is proposed for Yang-Mills theory. The procedure is based on a variant of dimensional regularization, called split dimensional regularization, which leads to internally consistent, ambiguity-free integrals. It is demonstrated that split dimensional regularization yields a one-loop Yang-Mills self-energy, ∏μvab, that is non-transverse, but local. Despite the non-covariant nature of the Coulomb gauge, ghosts are necessary in order to satisfy the appropriate Ward/BRS identity. The computed Coulomb-gauge Feynman integrals are applicable to both Abelian and non-Abelian gauge models.