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Analyticity domain of a quantum field theory and accelero-summation

  • Marc P. BellonEmail author
  • Pierre J. Clavier
Article
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Abstract

From ’t Hooft’s argument, one expects that the analyticity domain of an asymptotically free quantum field theory is horn shaped. In the usual Borel summation, the function is obtained through a Laplace transform and thus has a much larger analyticity domain. However, if the summation process goes through the process called acceleration by Écalle, one obtains such a horn-shaped analyticity domain. We therefore argue that acceleration, which allows to go beyond standard Borel summation, must be an integral part of the toolkit for the study of exactly renormalisable quantum field theories. We sketch how this procedure is working and what are its consequences.

Keywords

Renormalization Borel transform Alien calculus Accelero-summation 

Mathematics Subject Classification

81Q40 81T16 40G10 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique et Hautes Energies, LPTHESorbonne Université, CNRSParisFrance
  2. 2.MathematikPotsdam UniversitätGolmDeutschland

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