The combinatorics of Bogoliubov’s recursion in renormalization
Kurusch Ebrahimi-FardUniversité de Haute Alsace, Mulhouse, France
Dominique ManchonUniversité Blaise Pascal, Aubière, France
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We describe various combinatorial aspects of the Birkhoff–Connes–Kreimer factorization in perturbative renormalization. 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.