From geometric quantization to Moyal quantization

TL;DR

This paper demonstrates how geometric quantization techniques applied to a doubled phase space can derive the Moyal product and Weyl correspondence, linking geometric and phase-space quantization methods.

Contribution

It introduces a novel approach to derive Moyal quantization directly from geometric quantization on a symplectic groupoid.

Findings

Derivation of Moyal product from geometric quantization

Connection established between geometric and phase-space quantization

Use of symplectic groupoid structure in quantization methods

Abstract

We show how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic groupoid constructed by ``doubling'' the phase space.