Berezin-Toeplitz quantization and complex Weyl quantization of the torus \(\mathbb{T}^2\) (Q2413202)

Summary: 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 \(\mathbb{T}^2\).