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.

中文翻译：

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接触度量流形的灯芯型变形量化

我们构造了接触度量流形的 Wick 型变形量化。该结构是完全规范的，不涉及任意选择。与辛流形或泊松流形的情况不同，由于可能存在量子化障碍，并非一般接触度量流形上的每个经典可观测量都可以提升为量子流形。然而，我们证明所有这些障碍对于 Sasakian 流形来说都消失了。