Identification of Berezin-Toeplitz deformation quantization

2000/06/08 by Alexander Karabegov, Alexander V. Karabegov, Karabegov, Alexander V. +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math-ph #math.AG #math.CV #math.MP #math.QA #math.SG #msc:32C17 #msc:53C55 #msc:53D55 #msc:58F06 #msc:58G15 #msc:81S10 #quant-ph

paper · pdf · doi:10.48550/arxiv.math/0006063

26 pages

arxiv created 2000/06/08 · arxiv updated 2009/11/30

Abstract

We give a complete identification of the deformation quantization which was obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler manifold. The deformation quantization with the opposite star-product proves to be a differential deformation quantization with separation of variables whose classifying form is explicitly calculated. Its characteristic class (which classifies star-products up to equivalence) is obtained. The proof is based on the microlocal description of the Szegoe kernel of a strictly pseudoconvex domain given by Boutet de Monvel and Sjoestrand.

Cited by

• Quantization of Kähler manifolds via differential operators
• Optimal Remainder Estimates in the Quantization of Complex Projective Spaces

Related

• Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization
• Deformation quantization of compact Kähler manifolds via Berezin-Toeplitz operators
• A formal model of Berezin-Toeplitz quantization
• Berezin-Toeplitz Quantization of compact Kaehler manifolds
• Berezin-Toeplitz Quantization and Star Products for Compact Kaehler Manifolds