Deformation quantization of contact manifolds

TL;DR

This paper extends Fedosov deformation quantization to contact manifolds, revealing new invariants and highlighting differences from symplectic cases where not all observables are quantizable.

Contribution

It introduces a deformation quantization framework for contact manifolds and identifies obstructions and invariants unique to this setting.

Findings

Not all classical observables on contact manifolds are quantized.

New invariants of contact manifolds are discovered.

Obstructions to quantization are characterized.

Abstract

We extend Fedosov deformation quantization to general contact manifolds. Unlike the case of symplectic manifolds, not every classical observable on a contact manifold is generally quantized. On examination of possible obstructions to quantization, we obtain some new invariants of contact manifolds.