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

References in corpus (4)

• Mixable Shuffles, Quasi-shuffles and Hopf Algebras
• From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
• Equivariant Todd Classes for Toric Varieties
• Formulas for Birkhoff-(Rota-Baxter) decompositions related to connected bialgebra

Cited by in corpus (1)

• Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras