The bialgebra of specified graphs and external structures (Q461271)

Summary: 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 \textit{A. Connes} and \textit{D. Kreimer} [Commun. Math. Phys. 210, No. 1, 249--273 (2000; Zbl 1032.81026)] and the Birkhoff decomposition for two renormalization schemes: the minimal subtraction scheme and the Taylor expansion scheme.