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.
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Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01492967
Contributeur : Patras Frédéric <>
Soumis le : jeudi 5 juillet 2018 - 19:58:55
Dernière modification le : mercredi 10 octobre 2018 - 10:09:04

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  • HAL Id : hal-01492967, version 2
  • ARXIV : 1703.07304

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Frédéric Menous, Frédéric Patras. Renormalization: a quasi-shuffle approach. 2018. 〈hal-01492967v2〉

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