nLab metaplectic quantization

Idea

A variant of geometric quantization. Given a symplectic manifold equipped with Mp^c structure, metaplectic quantization forms instead of the geometric prequantum line bundle the symplectic spinor bundle and lets a symplectic Dirac operation induced by a choice of symplectic connection act on its sections (wavefunctions).

References

The original article is

• K. Habermann, An $Mp^c$-spinorial approach to a geometric-type quantization for symplectic manifolds, in Fritz Gesztesy, et al. (eds.), Stochastic processes, physics and geometry: New interplays, vol. II. CMS Conf. Proc. 29, 259-268 (2000).

Review includes

• Alexander Cardona, Geometric and Metaplectic quantization (pdf)