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

TL;DR

This paper develops a consistent formulation of dimensional regularization and minimal subtraction in Minkowski position space within perturbative Algebraic Quantum Field Theory, providing a forest formula solution for Epstein-Glaser renormalization.

Contribution

It introduces a novel implementation of DimReg and MS in position space and derives a forest formula for Epstein-Glaser renormalization within pAQFT.

Findings

Formulated DimReg and MS in Minkowski position space.

Derived a forest formula for Epstein-Glaser recursion.

Connected renormalization with Hopf algebra approaches.

Abstract

The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established.