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 ${\mathbb{T}}^2$.