The bialgebra of specified graphs and external structures

Abstract

We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantumfield 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 in [2] and the Birkhoff decomposition for two renormalization schemes: the minimal subtraction scheme and the Taylor expansion scheme.