Algebraic Birkhoff decomposition and its applications
arXiv:0807.2266
Abstract
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.
39 pages. To appear in "Automorphic Forms and Langlands Program"
References in corpus (6)
- Hopf algebras, from basics to applications to renormalization
- From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
- Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
- Renormalization of Multiple -Zeta Values
- Differential Birkhoff decomposition and the renormalization of multiple zeta values
- Operated semigroups, Motzkin paths and rooted trees
Cited by in corpus (6)
- Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
- Gauge Symmetries and Renormalization
- Structure theorems of mixable shuffle algebras and free commutative Rota-Baxter algebras
- Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
- Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations
- A Hopf algebra on subgraphs of a graph