2005/08/21 by Kurusch Ebrahimi‐Fard, K. Ebrahimi-Fard, Li Guo +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.hep-th/0508155
44 pages, some diagrams were generated with JAXODRAW
arxiv created 2005/08/21 · openalex publication_date 2005/08/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate the Hopf algebraic approach of Connes and Kreimer to renormalization in perturbative quantum field theory using triangular matrix representation. We give a Rota-Baxter anti-homomorphism from general regularized functionals on the Feynman graph Hopf algebra to triangular matrices with entries in a Rota-Baxter algebra. For characters mapping to the group of unipotent triangular matrices we derive the algebraic Birkhoff decomposition for matrices using Spitzer's identity. This simple matrix factorization is applied to characterize and calculate perturbative renormalization.