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Renormalization and Periods in Perturbative Algebraic Quantum Field Theory

  • Kasia RejznerEmail author
Conference paper
  • 34 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)

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.

Keywords

Quantum field theory Periods Epstein-Glaser renormalization 

Notes

Acknowledgements

I would like to thank ICMAT (Madrid) for hospitality and financial support. The ideas presented in this paper were developed during my stay in Madrid in 2014 as part of the “Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory”.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of YorkYorkUK

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