Abstract
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.
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Acknowledgements
The work of B.M.E. was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”. The work of A.A.Sh. was supported by the FAPESP Grant 2022/13596-8.
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Elfimov, B.M., Sharapov, A.A. Wick-type deformation quantization of contact metric manifolds. Lett Math Phys 114, 37 (2024). https://doi.org/10.1007/s11005-024-01787-y
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DOI: https://doi.org/10.1007/s11005-024-01787-y