Wilsonian renormalization , differential equations and Hopf algebras

  title={Wilsonian renormalization , differential equations and Hopf algebras},
  author={Thomas Krajewski and P. Martinetti},
In this paper, we present an algebraic formalism inspired by Butcher’s B-series in numerical analysis and the Connes-Kreimer approach to perturbative renormalization. We first define power series of non linear operators and propose several applications, among which the perturbative solution of a fixed point equation using the non linear geometric series. Then, following Polchinski, we show how perturbative renormalization works for a non linear perturbation of a linear differential equation… CONTINUE READING