Feynman Diagrams and Lax Pair Equations

Abstract

We find a Lax pair equation corresponding to the Connes-Kreimer Birkhoff factorization of the character group of a Hopf algebra. This flow preserves the locality of counterterms. In particular, we obtain a flow for the character given by Feynman rules, and relate this flow to the Renormalization Group Flow.

Rewritten and expanded version of math-ph/0611014

References in corpus (2)

• A Lie theoretic approach to renormalization
• Hopf algebras, from basics to applications to renormalization