In this paper, we give a correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the torus $ \mathbb{T}^2$. To achieve this, we use the correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the complex plane and a relation between the Berezin-Toeplitz quantization of a periodic symbol on the real phase space $\mathbb{R}^2$ and the Berezin-Toeplitz quantization of a symbol on the torus $ \mathbb{T}^2 $.

中文翻译：

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Berezin–Toeplitz 量化和环面的复 Weyl 量化 $\mathbb T^2$

在本文中，我们给出了圆环 $\mathbb{T}^2$ 的 Berezin-Toeplitz 和复 Weyl 量化之间的对应关系。为了实现这一点，我们使用了复平面的 Berezin-Toeplitz 和复 Weyl 量化之间的对应关系，以及实相空间 $\mathbb{R}^2$ 上周期符号的 Berezin-Toeplitz 量化和圆环上符号的 Berezin-Toeplitz 量化 $ \mathbb{T}^2 $。