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.
Dernière modification : Wednesday 06 July 2011 | Contact : Cyril.Banderier at lipn.univ-paris13.fr |