Split Dimensional Regularization for the Coulomb Gauge

A new procedure for regularizing Feynman integrals in the noncovariant Coulomb gauge 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 that is nontransverse, but local. Despite the noncovariant 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. PACS: 11.15, 12.38.CComment: 19 pages, 2 figures, 1 table, 72 references. This Replaced version clarifies why the Coulomb gauge requires a new type of regularization, and why our new regularization is compatible with Wick rotation. Results and table of integrals are unchanged. To appear in Nuclear Physics