Matrix Representation of Renormalization in Perturbative Quantum Field Theory

Abstract

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.

44 pages, some diagrams were generated with JAXODRAW

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Cited by in corpus (6)

• Rota-Baxter Algebras and Dendriform Algebras
• Free Rota-Baxter algebras and rooted trees
• Hopf algebra approach to Feynman diagram calculations
• Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
• The combinatorics of Bogoliubov's recursion in renormalization
• Representations of Rota-Baxter algebras and regular singular decompositions