Geometric quantization

Summary

Geometric quantization is a method to build a quantum system from a classical one, using the geometry of a symplectic manifold. It first attaches to the manifold a complex line bundle with a connection whose curvature is the symplectic form. Then it cuts down the space of sections of this bundle with a choice of polarization. The method was developed by Kostant and Souriau in the 1960s and 1970s, and it is closely tied to the orbit method in representation theory.