Geometric Quantization of Vector Bundles

Abstract

I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection on the bundle.

18 pages. AMS-LaTeX and AMS fonts (including Euler). Improvements to the main proof and notation. Reference [8] is math.QA/9811049

References in corpus (3)

• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Strict quantization of coadjoint orbits
• The Correspondence between Geometric Quantization and Formal Deformation Quantization

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• Pseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds
• The matrix regularization for Riemann surfaces with magnetic fluxes
• An Obstruction to Quantization of the Sphere
• Berezin quantization of noncommutative projective varieties
• Laplacians on Fuzzy Riemann Surfaces
• Deformation Quantization of Surjective Submersions and Principal Fibre Bundles
• Regularization of matrices in the covariant derivative interpretation of matrix models
• Morita equivalence bimodules for Wick type star products
• Quantization of Multiply Connected Manifolds
• Quantization of Yang--Mills metrics on holomorphic vector bundles