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Zeitschrift für Analysis und ihre Anwendungen


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Volume 11, Issue 4, 1992, pp. 437–454
DOI: 10.4171/ZAA/591

Published online: 1992-12-31

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

Hans G. Embacher[1], Gebhard Grübl[2] and Michael Oberguggenberger[3]

(1) Universität Innsbruck, Austria
(2) Universität Innsbruck, Austria
(3) Universität Innsbruck, Austria

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.

Keywords: Products of distributions, renormalization, Wightman distributions

Embacher Hans, Grübl Gebhard, Oberguggenberger Michael: Products of Distributions in Several Variables and Applications to Zero–Mass QED$_2$. Z. Anal. Anwend. 11 (1992), 437-454. doi: 10.4171/ZAA/591