An algebraic Birkhoff decomposition for the continuous renormalization group
High Energy Physics - Theory
2015-06-26 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/0401157,
title = {An algebraic Birkhoff decomposition for the continuous renormalization group},
author = {F. Girelli and T. Krajewski and P. Martinetti},
journal= {arXiv preprint arXiv:hep-th/0401157},
year = {2015}
}