12:00
How to evaluate meromorphic germs at their poles while preserving a
locality principle reminiscent of locality in QFT is a question that
lies at the heart of pQFT. It further arises in other disguises in
number theory, the combinatorics on cones and toric geometry. We
introduce an abstract notion of locality and a related notion of
mutually independent meromorphic germs in several variables. Much in the
spirit of Speer's generalised evaluators in the framework of analytic
renormalisation, the question then amounts to extending the ordinary
evaluation at a point to certain algebras of meromorphic germs, in
such a way that the extension factorises on mutually independent
germs. In the talk, we shall describe a family of such extended
evaluators and show that modulo a Galois type transformation, they
amount to a minimal subtraction scheme in several variables.
This talk is based on ongoing joint work with Li Guo and Bin Zhang.