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

November 21, 2013

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 Stueckelberg and Petermann.

Keywords:

*none*