Wick-type deformation quantization of contact metric manifolds

We construct a Wick-type deformation quantization of contact metric manifolds. The construction is fully canonical and involves no arbitrary choice. Unlike the case of symplectic or Poisson manifolds, not every classical observable on a general contact metric manifold can be promoted to a quantum on...

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Bibliographic Details
Published in:Letters in mathematical physics 2024-03, Vol.114 (2), Article 37
Main Authors: Elfimov, Boris M., Sharapov, Alexey A.
Format: Article
Language:English
Subjects:
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We construct a Wick-type deformation quantization of contact metric manifolds. The construction is fully canonical and involves no arbitrary choice. Unlike the case of symplectic or Poisson manifolds, not every classical observable on a general contact metric manifold can be promoted to a quantum one due to possible obstructions to quantization. We prove, however, that all these obstructions disappear for Sasakian manifolds.
ISSN:1573-0530
1573-0530
DOI:10.1007/s11005-024-01787-y