An algebraic Birkhoff decomposition for the continuous renormalization group

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.

References in corpus (9)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\beta$-function, diffeomorphisms and the renormalization group
• Integrable Renormalization II: the general case
• Runge-Kutta methods and renormalization
• Wave-Function renormalization and the Hopf algebra of Connes and Kreimer
• On the antipode of Kreimer's Hopf algebra
• On the Differential equations of the characters for the Renormalization group
• S-matrices for spinor particles on Reissner-Nordström black holes
• A Hopf algebra deformation approach to renormalization

Cited by in corpus (3)

• Combinatorial Hopf algebras in quantum field theory I
• Hopf algebra approach to Feynman diagram calculations
• The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras