On Weyl Quantization from geometric Quantization

Abstract

A. Weinstein has conjectured a nice looking formula for a deformed product of functions on a hermitian symmetric space of non-compact type. We derive such a formula for symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional symplectic manifolds: the euclidean plane, the sphere and the hyperbolic plane. For the euclidean plane we obtain the well known Moyal-Weyl product. The other cases show that Weinstein's original idea should be interpreted with care. We conclude with comments on the status of our result.

11 pages. (v2: corrected a couple of typos)

References in corpus (3)

• A variational principle for actions on symmetric symplectic spaces
• Heisenberg Evolution WKB and Symplectic Area Phases
• Cotangent bundle quantization: Entangling of metric and magnetic field

Cited by in corpus (5)

• Symbol correspondences for spin systems
• A variational principle for actions on symmetric symplectic spaces
• Symplectic Microgeometry III: Monoids
• Cotangent bundle quantization: Entangling of metric and magnetic field
• Strongly exponential symmetric spaces