25 May 2017 to 2 June 2017
Mainz Institute for Theoretical Physics, Johannes Gutenberg University
Europe/Berlin timezone

The locally convex Weyl algebra

31 May 2017, 10:00
1h
02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

02.430

Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Staudingerweg 9 / 2nd floor, 55128 Mainz

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.

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