An algebraic Birkhoff decomposition for the continuous renormalization group.

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing us to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited. [ABSTRACT FROM AUTHOR]