Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 08 février 2011 à 14h00 en B311, Pierre Martinetti nous parlera de : An algebraic Birkhoff decomposition for non perturbative renormalization

Résumé : An algebraic Birkhoff decomposition for non perturbative renormalization.
We show how the formalism of Connes-Kreimer, initially developed for perturbative renormalization, can be partially adapted to Wilson's continuous renormalization. The combinatorics of renormalization is no longer described by the Hopf algebra of Feynman diagrams, but rather by the Hopf algebra of rooted trees with two decorations. The latest correspond to the two distinct scales at which one fixes the initial conditions of the equations of the renormalization group. In this framework, we show that the equivalent of the projection on the holomorphic part of the Birkhoff decomposition (in perturbative renormalization) is now a projection on one decoration.

 [Slides.pdf]


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