The combinatorics of Bogoliubov's recursion in renormalization

Details The combinatorics of Bogoliubov's recursion in renormalization The combinatorics of Bogoliubov's recursion in renormalization

2007-10-19

arxiv.org/abs/0710.3675v2

Physics

Mathematical Physics

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

Scientific paper

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.

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