2006/02/28 by Kurusch Ebrahimi-Fard, K. Ebrahimi-Fard, Li Guo +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-006-0080-7
published as Comm. in Math. Phys. 267 no.3 (2006) 821-845 · accepted for publication in Comm. in Math. Phys
arxiv created 2006/03/14 · openalex publication_date 2006/08/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations. The unification is given by a Birkhoff type decomposition that was obtained from the Baker-Campbell-Hausdorff formula in our study of the Hopf algebra approach of Connes and Kreimer to renormalization in perturbative quantum field theory. There we showed that the Birkhoff decomposition of Connes and Kreimer can be obtained from a certain Baker-Campbell-Hausdorff recursion formula in the presence of a Rota-Baxter operator. We will explain how the same decomposition generalizes the factorization of formal exponentials and uniformization for Lie algebras that arose in vertex operator algebra and conformal field theory, and the even-odd decomposition of combinatorial Hopf algebra characters as well as to the Lie algebra polar decomposition as used in the context of the approximation of matrix exponentials in ordinary differential equations.