Renormalization: a quasi-shuffle approach
Abstract
In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with values in a Rota-Baxter algebra of amplitudes. We associate in this paper to any such algebra a universal semi-group (different in nature from the Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes associated to Feynman graphs produces the expected operations: Bogoliubov's preparation map, extraction of divergences, renormalization. In this process a key role is played by commutative and noncommutative quasi-shuffle bialgebras whose universal properties are instrumental in encoding the renormalization process.
Keywords
Cite
@article{arxiv.1703.07304,
title = {Renormalization: a quasi-shuffle approach},
author = {Frédéric Menous and Frédéric Patras},
journal= {arXiv preprint arXiv:1703.07304},
year = {2018}
}