JournalspmVol. 74, No. 4pp. 315–354

Berezin–Toeplitz quantization and complex Weyl quantization of the torus T2\mathbb T^2

  • Ophélie Rouby

    Universidade de Lisboa, Portugal
Berezin–Toeplitz quantization and complex Weyl quantization of the torus $\mathbb T^2$ cover

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Abstract

In this paper, we give a correspondence between the Berezin–Toeplitz and the complex Weyl quantizations of the torus T2\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 R2\mathbb R^2 and the Berezin–Toeplitz quantization of a symbol on the torus T2\mathbb T^2.

Cite this article

Ophélie Rouby, Berezin–Toeplitz quantization and complex Weyl quantization of the torus T2\mathbb T^2. Port. Math. 74 (2017), no. 4, pp. 315–354

DOI 10.4171/PM/2008