An algebraic Birkhoff decomposition for the continuous renormalization group

Details An algebraic Birkhoff decomposition for the continuous renormalization group An algebraic Birkhoff decomposition for the continuous renormalization group

2004-01-22

arxiv.org/abs/hep-th/0401157v1

J.Math.Phys. 45 (2004) 4679-4697

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

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 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.

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