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MP: Theoretische und Mathematische Grundlagen der Physik

MP 2: Quantenfeldtheorie und Strings

MP 2.1: Fachvortrag

Montag, 24. März 2003, 16:30–17:00, F309

On a relation between Bogoliubov’s renormalization operator and number theory — •Bertfried Fauser — Universität Konstanz, Fachbereich Physik, Fach M678, 78457 Konstanz

Recently a great progress is ongoing in an algebraic understanding of the renormalization process of quantum field theory. It was shown that the combinatorics of the Zimmermann forest formula can be understood in terms of cohomological algebra. Recursive and nonrecursive formulae for the convolutive inverse –in the case of the identity morphism yielding the antipode– were given. However, renormalization needs a second operation, the Bogoliubov renormalization operator, which causes the appearance of counter terms. These counter terms originate from analytical properties of the involved integrals. In this lecture we will show that there might be a deep link to number theory and the ring of number theoretic functions via the Möbius inversion, zeta-function and divisibility, which might open a purely algebraic approach to renormalization.