Berezin-Toeplitz quantization and complex Weyl quantization of the torus t²

Ophélie Rouby (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 GFMUL - Grupo de Fisica Matematica

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 $.

Mots clés: Berezin-Toeplitz quantization; Weyl quantization; Pseudo-differential operators; Bargmann transform

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Algèbres d'opérateurs [math.OA]; Géométrie symplectique [math.SG]

Ophélie Rouby. Berezin-Toeplitz quantization and complex Weyl quantization of the torus t². Portugaliae Mathematica, 2017, 74 (4), pp.315-354. ⟨10.4171/PM/2008⟩. ⟨hal-01471286⟩