Classification of systems of Dyson-Schwinger equations in the Hopf algebra of decorated rooted trees.

DOI10.1016/j.aim.2010.01.024zbMath1234.16024OpenAlexW1964355300MaRDI QIDQ981625

Loïc Foissy

Publication date: 1 July 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2010.01.024

zbMATH Keywords

quantum field theorypre-Lie algebrasConnes-Kreimer Hopf algebrasdecorated rooted treesHopf algebras of treessystems of combinatorial Dyson-Schwinger equations

Mathematics Subject Classification ID

Trees (05C05) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Applications of Lie (super)algebras to physics, etc. (17B81) Connections of Hopf algebras with combinatorics (16T30)

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Cites Work

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• Hopf-algebraic structure of families of trees
• Hopf-algebraic structure of combinatorial objects and differential operators
• Hopf algebras, renormalization and noncommutative geometry
• Normal coordinates and primitive elements in the Hopf algebra of renormalization
• Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
• Combinatorics of (perturbative) quantum field theory
• Finite dimensional comodules over the Hopf algebra of rooted trees
• Differential algebra structures on families of trees.
• Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations.
• On the structure of Hopf algebras
• Algèbres pré-Lie et algèbres de Hopf liées à la renormalisation
• ON THE ANTIPODE OF KREIMER'S HOPF ALGEBRA
• Combinatorics of rooted trees and Hopf algebras
• Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees