Superpropagator for a nonpolynomial field

Abstract

By using a method originally due to Okubo we calculate the momentum-space superpropagator for a nonpolynomial field U(x)=1/[1+fφ(x)] both for a massless and a massive neutral scalar φ(x) field. For the massless case we obtain a representation that resembles the weighted superposition of propagators for the exchange of a group of scalar fields φ(x) as is intuitively expected. The exact equivalence of this representation with the propagator function which has been obtained earlier through the use of the Fourier transform of a generalized function is established. For the massive case we determine the asymptotic form of the superpropagator.