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Loop of formal diffeomorphisms

Le : 06/12/2017 09h30
Par : Alessandra Frabetti (Lyon)
Lieu : I103
Lien web :
Résumé : In perturbative Quantum Field Theory, the renormalization of a scalar theory is encoded by the representative Hopf algebra of the so-called diffeographisms group [Connes-Kreimer 1998--2001], which boils down to the group of formal diffeomorphisms when we evaluate "physical" asymptotic series by summing up all Feynman graphs with a given number of vertices. Feynman graphs, and their partial sums, can then be seen as "global coordinates" for proalgebraic varieties of correlation functions and of renormalization factors. For non-scalar theories and in other QFT contexts, the functorial description of correlation functions and renormalization factors is preserved if we allow functors on non-commutative algebras, in the spirit of Kan 1959, Eckmann-Hilton 1961-1963, Bergman-Hausknecht 1996 and Fresse 1998. I present an application to formal diffeomorphisms, which further requires to replace groups by their non-associative versions called loops [Moufang 1935]. It is a joint work with Ivan P. Shestakov (Sao Paulo).