Rota–baxter Algebras in Renormalization of Perturbative Quantum Field Theory
نویسندگان
چکیده
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 review several aspects of Rota– Baxter algebras as they appear in other sectors also relevant to perturbative renormalization, for instance multiple-zeta-values and matrix differential equations. 2006 PACS Classification: 03.70.+k, 11.10.Gh, 02.10.Hh, 02.10.Ox, 02.20.Sv, 02.30.Hq
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A Noncommutative Bohnenblust–spitzer Identity for Rota–baxter Algebras Solves Bogoliubov’s Recursion
The Bogoliubov recursion is a particular procedure appearing in the process of renormalization in perturbative quantum field theory. It provides convergent expressions for otherwise divergent integrals. We develop here a theory of functional identities for noncommutative Rota–Baxter algebras which is shown to encode, among others, this process in the context of Connes–Kreimer’s Hopf algebra of ...
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