The combinatorics of Bogoliubov's recursion in renormalization
Mathematical Physics
2020-12-08 v2 High Energy Physics - Theory
Combinatorics
math.MP
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.
Keywords
Cite
@article{arxiv.0710.3675,
title = {The combinatorics of Bogoliubov's recursion in renormalization},
author = {Kurusch Ebrahimi-Fard and Dominique Manchon},
journal= {arXiv preprint arXiv:0710.3675},
year = {2020}
}
Comments
improved version, 20 pages, CIRM 2006 workshop "Renormalization and Galois Theory", Org. F. Fauvet, J.-P. Ramis