Portugaliae Mathematica


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Volume 74, Issue 4, 2017, pp. 315–354
DOI: 10.4171/PM/2008

Published online: 2018-02-08

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

Ophélie Rouby[1]

(1) Universidade de Lisboa, Portugal

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 $\mathbb T^2$.

Keywords: Quantization of the torus, Berezin–Toeplitz operators, pseudo-differential operators, Bargmann transform

Rouby Ophélie: Berezin–Toeplitz quantization and complex Weyl quantization of the torus $\mathbb T^2$. Port. Math. 74 (2017), 315-354. doi: 10.4171/PM/2008