Renormalization theory of Feynman amplitudes on configuration spaces

TL;DR

This paper extends a renormalization method for Feynman amplitudes from Euclidean to Minkowski space, integrating it with causal perturbation theory to advance quantum field theory calculations.

Contribution

It introduces a modified renormalization map theory suitable for Minkowski space and combines it with causal perturbation theory, enhancing the algebraic approach to quantum field renormalization.

Findings

Developed a Minkowski space adaptation of renormalization maps.

Integrated renormalization maps with causal perturbation theory.

Provided a framework for algebraic quantum field theory calculations.

Abstract

In a previous paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187) we presented a new method for renormalization in Euclidean configuration spaces based on certain renormalization maps. This approach is aimed to serve for developing an algebraic algorithm for computing the Gell--Mann--Low renormalization group action. In the present work we introduce a modification of the theory of renormalization maps for the case of Minkowski space and we give the way how it is combined with the causal perturbation theory.