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arXiv · 1211.4429

Combinatorial Hopf algebraic description of the multiscale renormalization in quantum field theory

Thomas Krajewski·Vincent Rivasseau·Adrian Tanasa
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Abstract

We define in this paper several Hopf algebras describing the combinatorics of the so-called multi-scale renormalization in quantum field theory. After a brief recall of the main mathematical features of multi-scale renormalization, we define assigned graphs, that are graphs with appropriate decorations for the multi-scale framework. We then define Hopf algebras on these assigned graphs and on the Gallavotti-Nicolò trees, particular class of trees encoding the supplementary informations of the assigned graphs. Several morphisms between these combinatorial Hopf algebras and the Connes-Kreimer algebra are given. Finally, scale dependent couplings are analyzed via this combinatorial algebraic setting.

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Thomas Krajewski, Vincent Rivasseau, Adrian Tanasa. 2013-06-10. Combinatorial Hopf algebraic description of the multiscale renormalization in quantum field theory. https://arxiv.org/abs/1211.4429

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