Dynkin operators and renormalization group actions in pQFT.

Abstract : Renormalization techniques in perturbative quantum field theory were known, from their inception, to have a strong combinatorial content emphasized, among others, by Zimmermann's celebrated forest formula. The present article reports on recent advances on the subject, featuring the role played by the Dynkin operators (actually their extension to the Hopf algebraic setting) at two crucial levels of renormalization, namely the Bogolioubov recursion and the renormalization group (RG) equations. For that purpose, an iterated integrals toy model is introduced to emphasize how the operators appear naturally in the setting of renormalization group analysis. The toy model, in spite of its simplicity, captures many key features of recent approaches to RG equations in pQFT, including the construction of a universal Galois group for quantum field theories.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [35 references]  Display  Hide  Download

Contributor : Patras Frédéric <>
Submitted on : Tuesday, November 25, 2008 - 12:39:19 PM
Last modification on : Friday, January 12, 2018 - 1:51:33 AM
Document(s) archivé(s) le : Monday, June 7, 2010 - 11:21:04 PM


Files produced by the author(s)


  • HAL Id : hal-00341511, version 1
  • ARXIV : 0811.4087



Patras Frédéric. Dynkin operators and renormalization group actions in pQFT.. Contemporary mathematics, American Mathematical Society, 2009, Vertex Operator Algebras and Related Areas, Eds M. Bergvelt, G. Yamskulna, W. Zhao, 497, pp.169-184. ⟨hal-00341511⟩



Record views


Files downloads