On the zero-mass superpropagator

A rigorous construction for the zero-mass exponential superpropagator is given. It is based on an explicit regularization of the propagator in coordinate space and a suitable choice of the coupling constant is taken in order to damp down the regularized superpropagator to an L2 function. By applying a Sommerfeld-Watson transformation and a Fourier transformation we are able to show that the regularized superpropagator tends, in an appropriate sense, both in momentum and coordinate space, to some localizable generalized function. Analytic continuation in the coupling constant shows the appearance of a logarithmic cut. By means of the regularization of the propagator and the special choice of the coupling constant we have neither to cut divergent integrals nor to pass to Euclidean region. Extensions to superpropagators which are formally written as entire functions of the propagator are given.