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Chapitre D'ouvrage Année : 2018

Renormalization: a quasi-shuffle approach

Résumé

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.
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Dates et versions

hal-01492967 , version 1 (20-03-2017)
hal-01492967 , version 2 (05-07-2018)

Identifiants

Citer

Frédéric Menous, Frédéric Patras. Renormalization: a quasi-shuffle approach. Celledoni, E. et al. Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium 2016. Springer (2018), pp.599-628, 2018. ⟨hal-01492967v2⟩
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