Dynkin operators and renormalization group actions in pQFT.Report as inadecuate




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1 JAD - Laboratoire Jean Alexandre Dieudonné

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.

keyword : renormalization groupe de renormalisation Dynkin operator pQFT renormalisation renormalization group





Author: Patras Frédéric -

Source: https://hal.archives-ouvertes.fr/



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