On matrix differential equations in the Hopf algebra of renormalization

We establish Sakakibara's differential equations [M. Sakakibara, On the differential equations of the characters for the renormalization group, Mod. Phys. Lett. A 19 (2004), 1453.] 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.

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Published 1 January 2006