Products of Distributions in Several Variables and Applications to Zero–Mass QED${}_2$

Abstract

We study products of distributions in several variables, having in mind applications to quantum electrodynamics. We introduce a new product, the parameter product, and relate it to known ones. It allows us to rigorously interpret and evaluate products arising in the computations of the one-loop vacuum polarization of zero-mass QED${}_2$ , thereby avoiding the occurrence of renormalization ambiguities from the very beginning.