We extend the results we obtained in an earlier work . The cocommutative case of ladders is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the Birkhoff decomposition of renormalization theory is derived by using the double Rota-Baxter construction, respectively Atkinson's theorem. We also outline the extension to the Hopf algebra of Feynman graphs via decorated rooted trees.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics