On Dequantization of Fedosov's Deformation Quantization

Abstract

To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of the cotangent bundle to M to the formal neighborhood of the diagonal of the product M x M~, where M~ is a copy of M with the opposite Poisson structure. We call it dequantization of the natural deformation quantization. Then we "dequantize" Fedosov's quantization.

16 pages, latex; references, terminology, notation, and several typos corrected; to appear in "Letters in Math. Phys."

References in corpus (4)

• A path integral approach to the Kontsevich quantization formula
• Poisson sigma models and deformation quantization
• Fedosov Deformation Quantization as a BRST Theory
• Wick type deformation quantization of Fedosov manifolds

Cited by in corpus (7)

• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Formal symplectic groupoid
• Formal symplectic groupoid of a deformation quantization
• The Algebraic Index Theorem and Fedosov Quantization of Lagrange-Finsler and Einstein Spaces
• Fedosov's formal symplectic groupoids and contravariant connections
• On the inverse mapping of the formal symplectic groupoid of a deformation quantization
• Infinitesimal deformations of a formal symplectic groupoid