Application of finite field-dependent BRS transformations to problems of the Coulomb gauge

We discuss the Coulomb propagator in the formalism developed recently in which we construct the Coulomb gauge path-integral by correlating it with the well-defined Lorentz gauge path-integrals through a finite field-dependent BRS transformation. We discover several features of the Coulomb gauge from it. We find that the singular Coulomb gauge has to be treated as the gauge parameter lambda --> 0 limit. We further find that the propagator so obtained has good high energy behavior (k(0)(-2)) for lambda not equal 0 and epsilon not equal 0. We also find that the behavior of the propagator so obtained is sensitive to the order of limits k(0) --> infinity, lambda --> 0 and epsilon --> 0; so that these have to be handled carefully in a higher loop calculation. We show that we can arrive at the result of Cheng and Tsai for the ambiguous two-loop Feynman integrals without the need for an extra ad hoc regularization and within the path integral formulation.