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

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 Stueckelberg and Petermann.

51 pages, to be published in Journal of Mathematical Physics

References in corpus (3)

• Removal of violations of the Master Ward Identity in perturbative QFT
• Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization
• Perturbative Algebraic Quantum Field Theory and the Renormalization Groups

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