Matrix Representation of Renormalization in Perturbative Quantum Field Theory
نویسندگان
چکیده
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. 2001 PACS Classification: 03.70.+k, 11.10.Gh, 02.10.Hh, 02.10.Ox
منابع مشابه
Rota–baxter Algebras in Renormalization of Perturbative Quantum Field Theory
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota–Baxter algebras enters the scene. In this note we revi...
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