Abstract

CLAVIER, Pierre; GUO, Li; PAYCHA, Sylvie  and  ZHANG, Bin. Renormalisation via locality morphisms. Rev.colomb.mat. [online]. 2019, vol.53, suppl.1, pp.113-141.  Epub Mar 24, 2020. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v53nsupl.84010.

This is a survey on renormalisation in algebraic locality setup highlighting the role that locality morphisms can play for renormalisation purposes. After describing the general framework to build locality regularisation maps, we illustrate renormalisation by locality algebra homomorphisms on three examples, the renormalisation of conical zeta functions at poles, the definition of branched zeta functions and their evaluation at poles and finally the values of iterated integrals stemming from Kreimer's toy model.

Keywords : locality; renormalisation; partial algebra; operated algebra; Hopf algebra; Rota-Baxter algebra; symbols.

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