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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
10/2006

Renormalization : A number theoretical model

Bertfried Fauser

Abstract

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.

Received:
Jan 25, 2006
Published:
Jan 25, 2006
MSC Codes:
16W30, 30B50, 11A15, 81T15, 81T16
Keywords:
hopf algbera, renormalization, dirichlet series, dirichlet convolution, multiplicative arithmetic functions

Related publications

inJournal
2008 Journal Open Access
Bertfried Fauser

Renormalization : a number theoretical model

In: Communications in mathematical physics, 277 (2008) 3, pp. 627-641