# Berezin-toeplitz quantization and complex weyl quantization of the torus t${}^2$

## TL;DR

This paper establishes a connection between Berezin-Toeplitz and complex Weyl quantizations specifically for the torus, extending known relations from the complex plane and real phase space to the toroidal setting.

## Contribution

It introduces a novel correspondence between Berezin-Toeplitz and complex Weyl quantizations on the torus, building on existing relations in the complex plane and real phase space.

## Key findings

- Established a correspondence between Berezin-Toeplitz and complex Weyl quantizations of the torus
- Extended relations from the complex plane to the toroidal setting
- Linked quantizations of periodic symbols on the real phase space and the torus

## 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 $.