Products of Distributions in Several Variables and Applications to Zero-Mass QED2

H. G. Embacher, G. Grübl
Institut für Theoretische Physik der Universität Innsbruck,
A-6020 Innsbruck, Technikerstr. 25, Austria

M. Oberguggenberger
Institut für Mathematik und Geometrie der Universität Innsbruck,
A-6020 Innsbruck, Technikerstr. 13, Austria

(Received: 18. 02. 1992)

Abstract. We study products of distributions in serveral 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 QED2 , thereby avoiding the occurrence of renormalization ambiguities from the very beginning.

Key words. Products of distributions, renormalization, Wightman distributions.

AMS subject classification. 46F10, 81T40, 81T50.

Z. Anal. Anw. 11, 437 - 454 (1992).

Preprint. pdf-file, 13 pages, 260 kB.