Berezin–Toeplitz quantization and complex Weyl quantization of the torus $\mathbb T^2$

Abstract

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 $.