An algebraic formulation of the locality principle in renormalization
- An algebraic formulation of the locality principle in renormalization
- 2018-06-07 16:00-17:00
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 Euter-Maclaurin formula on lattice cones, we renormalize the exponential generating function which sums over the lattice points in a lattice cone.