On matrix differential equations in the Hopf algebra of renormalization

Kurusch Ebrahimi-Fard, Dominique Manchon
2006 Advances in Theoretical and Mathematical Physics  
We establish Sakakibara's differential equations in a matrix setting for the counter term (respectively renormalized character) in Connes-Kreimer's Birkhoff decomposition in any connected graded Hopf algebra, thus including Feynman rules in perturbative renormalization as a key example.
doi:10.4310/atmp.2006.v10.n6.a3 fatcat:akzufekugrazndpgjajft6l36a