BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alessandra Frabetti (Universite’ de Lyon 1) DTSTART:20210628T150000Z DTEND:20210628T160000Z DTSTAMP:20260423T053138Z UID:NCGandPH/6 DESCRIPTION:Title: Noncommutative renormalization Hopf algebras\nby Alessandra Frabetti (Universite’ de Lyon 1) as part of Noncommutative Geometry and Physics\n \n\nAbstract\nIn pQFT\, the renormalization group acts on the Lagrangian a s a group of formal diffeomorphisms in the powers of the coupling constant \, by substitution of the bare coupling and multiplication by some renorma lization factors built on the counterterms of divergent Feynman graphs.\n\ nFor scalar theories\, such groups are proalgebraic (functorial on the coe fficients algebra) and are represented by Faà di Bruno types of Hopf alge bras on graphs\, called renormalization Hopf algebras. In this talk I revi ew Connes-Kreimer's settings and comment on the improvements expected for the BPHZ formula which computes the counterterms of the graphs.\n\nFor non -scalar theories\, Feynman graphs have matrix-valued amplitudes: even if t he counterterms are scalar-valued\, the renormalization group cannot be re presented by a Hopf algebra in a functorial way\, because associativity fa ils for the composition of series with non-commutative coefficients. Both commutative and noncommutative renormalization Hopf algebras can be define d\, with different meanings. In this talk I explain in which sense the fir st ones are not functorial (hence not universal) and how the second ones r equire a functorial extension of proalgebraic groups to non-commutative al gebras which can only be done as "non-associative" groups.\n\nThe talk is based on Connes-Kreimer's results (2000)\, on joint works with Christian B rouder (2000-2006) and on the recent paper https://doi.org/10.1016/j.aim.2 019.04.053\n LOCATION:https://researchseminars.org/talk/NCGandPH/6/ END:VEVENT END:VCALENDAR