On the exponential superpropagator

Abstract

Series developments for distributions of the type Raexp( − κ2/R) (with R = r2 − t2) are discussed in the light of the Gel'fand-Shilov method for the definition of causal distributions. It is shown that there is no arbitrariness in the series. In Sec. I the concept of causal distribution is reviewed, in Sec. II the series developments are given, fixing the values of the constants in the □nδ terms. In Sec. III the Fourier transforms are computed. In Sec. IV we obtain the series development for the Fourier transform of exp( − κ2/R)∂μ ∂ν(R−1).