Kahler Quantization and Physics

May 2021

talk expository slides

Summary:

Geometric quantization associates a Kahler manifold to a vector space of holomorphic sections of a line bundle. By taking higher and higher powers of the line bundle, there are more and more holomorphic sections. In the limit, each point on the manifold sits in CP infinity by the Kodira embedding. These are coherent states, acting as quantum analogous of a classical point particle. This strategy is very useful in pure Kahler geometry.

Presented at:

MATH868C, Complex Geometry, UMD, Spring 2021