Speaker
Prof.
Stefan Waldmann
(Universität Würzburg)
Description
In my talk I will report on recent progesses in understanding the convergence
properties of certain examples of star products. For the Weyl-Moyal star
products on a Poisson vector space and its variations one obtains a
quantization for a large class of real-analytic functions leading to a locally
convex algebra containing elements with canonical commutation relations
specified by the constant Poisson structure. Depending on the analytic
properties of the Poisson vector space, the resulting algebra has many nice
properties which I will point out. The analytic structure of the algebra then
helps to prove self-adjointness of linear and quadratic elements in all GNS
representations in a very systematic way. Applications to quantum field theory
arise when the underlying Poisson vector space is the space of solutions to
linear wave equations.
