293 research outputs found
On matrix differential equations in the Hopf algebra of renormalization
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.Comment: 22 pages, typos correcte
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