Speaker: Prof.Li Guo (Rutgers University – Newark)

Title:An algebraic formulation of the locality principle in renormalization

Time: Mon. Fri. 21, 2018 , PM:4:00-5:00.

Location: Room 4318, Building No.4, Wushan Campus

 Abstract:

      An interpretation of the locality principle in renormalization is that a locality property is preserved in the process of renormalization. We establish such a principle in the framework of the algebraic approach of Connes and Kreimer to quantum field renormalization, by working with their algebraic Birkhoff factorization. More preciselly we show that if a regularization map is a locality map, then so is the corresponding renormalization map from the algebraic Birkhoff factorization. For this purpose, we introduce locality for various algebraic structures including those of a Hopf algebra, a Rota-Baxter algebra and a regularization map between the two algebras. As an application  in the context of the Euler-Maclaurin formula on lattice cones, we renormalize the exponential generating function which sums over the lattice points in a lattice cone.