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Dimensional Regularization in Position Space, and a Forest Formula for Epstein-Glaser Renormalization
Michael Dütsch, Klaus Fredenhagen, Kai Johannes Keller and Katarzyna Rejzner
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.