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:arXiv.org 2023-11
Main Authors: Elfimov, Boris M, Sharapov, Alexey A
Format: Article
Language:English
Subjects:
Deformation
Manifolds (mathematics)
Obstructions
Online Access:Get full text
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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:2331-8422