A Locality Principle of Renormalization via Algebraic Birkhoff Factorization

01.12.2017, 11:00 Uhr  –  Haus 31, Raum 0.18
Arbeitsgruppenseminar Analysis

Li Guo (Rutgers University)

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 precisely we show that if a regularization map is
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. For application, we consider the exponential generating function of lattice points in a convex cone, giving rise to a meromorphic function with linear poles.