Split dimensional regularization for the Coulomb gauge at two loops

We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy Sigma (p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters sigma and n/2 - sigma for the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that the overall coefficient of the leading pole term for Sigma (p) is strictly local. Extensive tables showing the pole parts of one- and two-loop Coulomb integrals are given. We also comment on some general implications of split dimensional regularization, discussing in particular the limit sigma --> 1/2 and the subleading terms in the E-expansion of noncovariant integrals. (C) 2000 Elsevier Science B.V. All rights reserved.