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| XXXIX Workshop on Geometric Methods in Physics | 19.06–25.06.2022 |
| XI School on Geometry and Physics | 27.06–1.07.2022 |
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Ziemowit DomańskiDeformation quantization on the cotangent bundle of a Lie groupA 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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| University of Bialystok |
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