Bialgebra of specified graphs and external structures

Dominique Manchon (1) , Mohamed Belhaj (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 GAAO

We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantum field theory. We introduce a convolution product and a semigroup of characters of this Hopf algebra with values in some suitable commutative algebra taking momenta into account. We then implement the renormalization described by A. Connes and D. Kreimer and the Birkhoff decomposition for two renormalization schemes: the minimal subtraction scheme and the Taylor expansion scheme.

Mots clés: Birkhoff decomposition; convolution; Bialgebras; Hopf algebras; graphs; renormalization

Domaines: Algèbres quantiques [math.QA]

Dominique Manchon, Mohamed Belhaj. Bialgebra of specified graphs and external structures. Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2014. ⟨hal-00835369v2⟩