The combinatorics of Bogoliubov's recursion in renormalization

Abstract

We describe various combinatorial aspects of the Birkhoff-Connes-Kreimer factorization in perturbative renormalisation. The analog of Bogoliubov's preparation map on the Lie algebra of Feynman graphs is identified with the pre-Lie Magnus expansion. Our results apply to any connected filtered Hopf algebra, based on the pro-nilpotency of the Lie algebra of infinitesimal characters.

improved version, 20 pages, CIRM 2006 workshop "Renormalization and Galois Theory", Org. F. Fauvet, J.-P. Ramis

References in corpus (9)

• Loday-type Algebras and the Rota-Baxter Relation
• A Lie theoretic approach to renormalization
• A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion
• Hopf algebras, from basics to applications to renormalization
• New identities in dendriform algebras
• From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
• Rota-Baxter algebras and new combinatorial identities
• Combinatorics of renormalization as matrix calculus
• Matrix Representation of Renormalization in Perturbative Quantum Field Theory

Cited by in corpus (4)

• A Zassenhaus-type algorithm solves the Bogoliubov recursion
• Algebra for quantum fields
• Dynkin operators and renormalization group actions in pQFT
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory