Differential Birkhoff decomposition and the renormalization of multiple zeta values

Abstract

In the Hopf algebra approach of Connes and Kreimer on renormalization of quantum field theory, the renormalization process is views as a special case of the Algebraic Birkhoff Decomposition. We give a differential algebra variation of this decomposition and apply this to the study of multiple zeta values.

20 pages

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Cited by in corpus (6)

• Algebraic Birkhoff decomposition and its applications
• Explicit double shuffle relations and a generalization of Euler's decomposition formula
• Double shuffle relations and renormalization of multiple zeta values
• Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras
• Analytic renormalization of multiple zeta functions. Geometry and combinatorics of the generalized Euler reflection formula for MZV
• Localization of Rota-Baxter algebras