Renormalization and periods in perturbative Algebraic Quantum Field Theory

2016/03/09 by Rejzner, Kasia
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1603.02748

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 β-function.

Related

• Periods and Hodge structures in perturbative quantum field theory
• Perturbative Algebraic Quantum Field Theory and the Renormalization Groups
• Perturbative Construction of Models of Algebraic Quantum Field Theory
• Quantum fields, periods and algebraic geometry
• Renormalization Hopf algebras and combinatorial groups