题目：Algebraic Birkhoff Factorization and Group Action in Renormalization
报告人：Professor Li Guo (Rutgers University Newark)
摘要: The Algebraic Birkhoff Factorization (ABF) of Connes and Kreimer gives an algebraic formulation of the renormalization process in quantum field theory. Their ABF is an factorization of an algebra homomorphism from a Hopf algebra to a Rota-Baxter algebra. This algebraic formulation facilitates the mathematical study in renormalization and allows the renormalization method to be applied to problems in mathematics.
In this talk we first give an introduction to ABF with a baby model for renormalization of Riemann integrals. We then give generalize ABF to locality Hopf algebras. This is an interpretation of the locality principle in renormalization, stating that a locality property is preserved in the process of renormalization. More precisely we show that if a regularization map is a locality map, then so is the corresponding renormalization map from the algebraic Birkhoff factorization. Group actions on ABF are also considered. As an application, we again consider the baby model.
This is a joint work with P. Clavier, S. Paycha and B. Zhang.
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