  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 \to 1/2 and the subleading terms in the
epsilon-expansion of noncovariant integrals.
