Renormalization and periods in perturbative Algebraic Quantum Field Theory

Abstract

In this paper I give an overview of mathematical structures appearing in perturbative algebraic quantum field theory (pAQFT) in the case of the massless scalar field on Minkowski spacetime. I also show how these relate to Kontsevich-Zagier periods. Next, I review the pAQFT version of the renormalization group flow and reformulate it in terms of Feynman graphs. This allows me to relate Kontsevich-Zagier periods to numbers appearing in computing the pAQFT $\beta$-function.

arXiv comment28 pages, to be published in the proceeding volume of the "Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory" in ICMAT (Madrid). Some typos corrected in this version and the proof of proposition 4.9 was expanded