Geoquant 2021 - Summer School
Abstract:
In my lecture series I will discuss the need of convergence for formal star products if one is interested in an honest quantum mechanical application of deformation quantization. Several competing approaches will be compared. In a series of examples I will advocate to take the series serious. Convergence and continuity of the star products can be shown in several important cases.
1.Deformation quantization and formal star products
2.First example: Convergence in the flat case
3.An application to field theory
4.Second example: Linear Poisson structures and the Gutt star product
5.More examples: Cotangent bundle of a Lie group, Poincaré disc, and beyond
