THE 3-POINT FUNCTION IN SPLIT DIMENSIONAL REGULARIZATION IN THE COULOMB GAUGE

We use a gauge-invariant regularization procedure, called split dimens ional regularization, to evaluate the quark self-energy Sigma(p) and q uark-quark-gluon vertex function Lambda(mu) (p',p) in the Coulomb gaug e, del.A(a) = 0. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian t heories. The technique which is based on two complex regulating parame ters, omega and sigma, is shown to generate a well-defined set of Coul omb-gauge integrals, A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, s ome of which are non local. It is further argued that the standard one -loop BRST identity relating Sigma and Lambda(mu), should by rights be replaced by a more general BRST identity which contains two additiona l contributions from ghost vertex diagrams. Despite the appearance of non-local Coulomb integrals, both Sigma and Lambda(mu), are local func tions which satisfy the appropriate BRST identity. Application of spli t dimensional regularization to two-loop energy integrals is briefly d iscussed. (C) 1998 Elsevier Science B.V.