An algebraic formulation of the locality principle in renormalisation - Archive ouverte HAL
Article Dans Une Revue European Journal of Mathematics Année : 2018

An algebraic formulation of the locality principle in renormalisation

Li Guo
  • Fonction : Auteur
Sylvie Paycha
  • Fonction : Auteur
Bin Zhang
  • Fonction : Auteur

Résumé

We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on cones, we renormalise the exponential generating function which sums over the lattice points in convex cones. For a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate functions.
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Dates et versions

hal-04131719 , version 1 (16-06-2023)

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Citer

Pierre Clavier, Li Guo, Sylvie Paycha, Bin Zhang. An algebraic formulation of the locality principle in renormalisation. European Journal of Mathematics, 2018, 5, pp.356-394. ⟨10.48550/arXiv.1711.00884⟩. ⟨hal-04131719⟩

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