Algebraic Birkhoff decomposition and its applications

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Guo, Li
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Central in the Hopf algebra approach to the renormalization of perturbative quantum field theory of Connes and Kreimer is their Algebraic Birkhoff Decomposition. In this tutorial article, we introduce their decomposition and prove it by the Atkinson Factorization in Rota-Baxter algebra. We then give some applications of this decomposition in the study of divergent integrals and multiple zeta values.
Comment: 39 pages. To appear in "Automorphic Forms and Langlands Program"
Keywords
Mathematics - Rings and Algebras, Mathematical Physics, Mathematics - Combinatorics, Mathematics - Number Theory, 11M41, 16W30, 16W99, 81T15
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