The combinatorics of Bogoliubov's recursion in renormalization

Kurusch Ebrahimi-Fard, Dominique Manchon
Arxiv ID: 0710.3675Last updated: 12/8/2020
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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