A nondiagrammatic description of the Connes-Kreimer Hopf algebra.

DOI10.1016/j.jpaa.2012.06.027zbMath1271.16033arXiv1203.2686OpenAlexW2964179466MaRDI QIDQ1946181

Alastair Hamilton

Publication date: 18 April 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.2686

zbMATH Keywords

Hopf algebras of Feynman graphspre-Lie algebras of Feynman graphspre-Lie algebras of polynomial vector fields

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Lie algebras of vector fields and related (super) algebras (17B66) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Hopf algebras and their applications (16T05) Connections of Hopf algebras with combinatorics (16T30)

Related Items (1)

A Poincar\'e-Birkhoff-Witt Theorem for profinite pronilpotent Lie algebras

Cites Work

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• Proof of the Bogoliubov-Parasiuk theorem on renormalization
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• Über die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder
• Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• On the structure of Hopf algebras
• Convergence of Bogoliubov's method of renormalization in momentum space
• Renormalization

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