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arxiv: math-ph/0606039 · v2 · pith:Q6S2CWVWnew · submitted 2006-06-16 · 🧮 math-ph · hep-th· math.MP

On matrix differential equations in the Hopf algebra of renormalization

classification 🧮 math-ph hep-thmath.MP
keywords algebradifferentialequationshopfmatrixrenormalizationbirkhoffcharacter
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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.

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