Séminaire Lotharingien de Combinatoire, B70c (2014), 23 pp.
Thomas Krajewski, Vincent Rivasseau and Adrian Tanasa
Combinatorial Hopf Algebraic Description of the Multi-Scale Renormalization
in Quantum Field Theory
We define combinatorial Hopf algebras on
assigned Feynman graphs and on Gallavotti-Nicol\`o trees,
which we then prove to underly the multi-scale renormalization in quantum field theory.
Moreover, homomorphisms between these Hopf algebras and the Connes-Kreimer Hopf algebras
on rooted trees and on
Feynman graphs are given. Finally, we show how this formalism can be used to investigate some algebraic properties of the effective expansion in multi-scale renormalization.
Received: June 6, 2013.
Revised: November 6, 2013.
Accepted: November 6, 2013.
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