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 (6)

• Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\beta$-function, diffeomorphisms and the renormalization group
• A Lie theoretic approach to renormalization
• Integrable Renormalization II: the general case
• An Étude in non-linear Dyson--Schwinger Equations
• Hopf algebras, from basics to applications to renormalization
• Using the Hopf Algebra Structure of QFT in Calculations

Cited by in corpus (1)

• Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations