Kolloquium: Sylvie Paycha (Universität Potsdam): Variations on Locality

Variations on Locality - Vortragende: Sylvie Paycha, Universität Potsdam – Einladender: K.-H. Neeb

Abstract: The principle of locality in quantum field theory states
that an object is influenced directly only by its immediate surroundings. We
introduce locality relations, defined as symmetric binary relations, which capture
essential features of locality. Correspondingly we define locality morphisms,
namely maps that factorise on products of pairs in the graph of such locality
relations. This factorisation is a key property in the context of
renormalisation, which served as a motivation for us to introduce the notation
of locality in the first place. I will show its efficiency when counting
lattice points inside a cone. This a priori infinite cardinal can naturally be
renormalised by implementing a regularisation in several variables. There
locality plays an essential role in avoiding fake finite
contributions. It enables a minimal subtraction scheme in several
variables which singles out a relevant finite part from the a priori infinite
cardinal. This is based on joint work with Li Guo (Rutgers, Newark) and Bin
Zhang (Sichuan U., Chengdu).