Convergence of Star Products: Examples and Concepts.

Stefan Waldmann (Julius Maximilian University Würzburg)

22-Feb-2021, 15:00-16:00 (3 years ago)

Abstract: In usual formal deformation quantization one considers formal deformations of the algebra of functions on a Poisson manifold viewing them as observables of a mechanical system whose quantum version one is interested in. However, there is yet another interpretation in terms of noncommutative geometry: the noncommutative products can be viewed as models of noncommutative manifolds, which, in turn, can be used for describing space-time geometry at small distances etc.

While formal deformation quantization has very general existence and classification results by Kontsevich's formality theorem, it lacks the immediate applicability to physical problems: the deformation parameter (e.g. Planck's constant $\hbar$ or the Planck length etc.) are formal only. Thus the understanding of the (non-) convergence of the formal series is one of the most important issues if one is interested in finding more realistic models beyond an "infinitesimal" deformation. Here in the recent years several classes of examples have been discussed. In my talk I will report on some of these examples illustrating the underlying geometry as well as some of the quite involved functional-analytic questions.

mathematical physics

Audience: researchers in the topic


Noncommutative Geometry and Physics

Series comments: Noncommutative geometry is a very general mathematical paradigm arising from quantum mechanics. As such, it permeates different branches of mathematics and physics.

The series of monthly talks accompanies the special issue of Journal of Physics A and is intended to present the many facets of the emergence of noncommutativity in physics.

Past seminars can be viewed on YouTube channel.

Organizers: Francesco D'Andrea*, Paolo Aschieri, Edwin Beggs, Emil Prodan, Andrzej Sitarz*
*contact for this listing

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