Geodesic
Combinatorial Hopf Algebraic Description of the Multi-Scale Renormalization in Quantum Field Theory
Séminaire lotharingien de combinatoire, Tome 70 (2013-2014) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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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. 

@article{SLC_2013-2014_70_a2,
     author = {Thomas Krajewski and Vincent Rivasseau and Adrian Tanasa},
     title = {Combinatorial {Hopf} {Algebraic} {Description} of the {Multi-Scale} {Renormalization} in {Quantum} {Field} {Theory}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2013-2014},
     volume = {70},
     url = {http://geodesic.mathdoc.fr/item/SLC_2013-2014_70_a2/}
}
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AU  - Vincent Rivasseau
AU  - Adrian Tanasa
TI  - Combinatorial Hopf Algebraic Description of the Multi-Scale Renormalization in Quantum Field Theory
JO  - Séminaire lotharingien de combinatoire
PY  - 2013-2014
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Thomas Krajewski; Vincent Rivasseau; Adrian Tanasa. Combinatorial Hopf Algebraic Description of the Multi-Scale Renormalization in Quantum Field Theory. Séminaire lotharingien de combinatoire, Tome 70 (2013-2014). http://geodesic.mathdoc.fr/item/SLC_2013-2014_70_a2/