Berezin-toeplitz quantization and complex weyl quantization of the torus t²

2017/02/20 by Rouby, Ophélie
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1702.05978

Abstract

In this paper, we give a correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the torus \mathbbT². 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 and the Berezin-Toeplitz quantization of a symbol on the torus \mathbbT² .

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