XXXIX Workshop on Geometric Methods in Physics 19.06–25.06.2022
XI School on Geometry and Physics 27.06–1.07.2022
In order to secure the right conditions for our Workshop we have decided to exceptionally move (only for this year's meeting) the site of our Workshop to the campus of our University in Białystok.

Ziemowit Domański


Deformation quantization on the cotangent bundle of a Lie group


A complete theory of non-formal deformation quantization on the cotangent bundle of a Lie group is presented. The starting point of the construction is a pre-C*-algebra of observables being a deformation of the classical pre-C*-algebra of observables. The deformed product from this algebra (the star-product) is introduced by means of an appropriate integral formula. Basic properties of the star-product are proved and the pre-C*-algebra is extended to a Hilbert algebra and an algebra of distributions. The algebra of distributions contains functions representing all observables interesting from a physical point of view. An operator representation in position space is constructed. The theory is illustrated on the example of the quantization of a rigid body.







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