Dimensional Regularization in Position Space, and a Forest Formula for Epstein-Glaser Renormalization

Michael Dütsch, Klaus Fredenhagen, Kai Johannes Keller, and Katarzyna Rejzner

Contact the author: Please use for correspondence this email.
Submission date: 19. Dec. 2013
Pages: 52
published in: Journal of mathematical physics, 55 (2014) 12, art-no. 122303 
DOI number (of the published article): 10.1063/1.4902380
Bibtex
Download full preprint: PDF (648 kB)

Abstract:
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. For scalar fields the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.