Renormalization in connected graded Hopf algebras: an introduction
نویسندگان
چکیده
We give an account of the Connes-Kreimer renormalization in the context of connected graded Hopf algebras. We first explain the Birkhoff decomposition of characters in the more general context of connected filtered Hopf algebras, then specializing down to the graded case in order to introduce the notions of locality, renormalization group and Connes-Kreimer’s Beta function. The connection with Rota-Baxter and dendriform algebras will also be outlined. This introductory/survey article is based on joint work with Kurusch Ebrahimi-Fard, Li Guo and Frédéric Patras ([19], [16], [21], [22], [23]).
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Hopf algebras, from basics to applications to renormalization
These notes are an extended version of a series of lectures given at Bogota from 2nd to 6th december 2002. They aim to present a self-contained introduction to the Hopf-algebraic techniques which appear in the work of A. Connes and D. Kreimer on renormalization in Quantum Field Theory [CK1], [CK2], [BF]... Our point of view consists in revisiting a substantial part of their work in the abstract...
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