Renormalization : A number theoretical model

Details Renormalization : A number theoretical model Renormalization : A number theoretical model

2006-01-25

arxiv.org/abs/math-ph/0601053v1

Commun.Math.Phys.277:627-641,2008

Physics

Mathematical Physics

15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 2005

Scientific paper

10.1007/s00220-007-0392-2

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.

Affiliated with

Also associated with

No associations

Rating

Renormalization : A number theoretical model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Renormalization : A number theoretical model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Renormalization : A number theoretical model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-405011