Geometric quantization; a crash course

TL;DR

This paper provides an accessible introduction to geometric quantization, covering fundamental concepts and mathematical tools necessary for understanding the process of quantizing classical systems.

Contribution

It offers a concise, lecture-based overview of geometric quantization, including category theory and densities, aimed at graduate students and newcomers.

Findings

Clarifies key concepts in geometric quantization

Provides foundational mathematical background

Serves as an educational resource for students

Abstract

Early in 2011 Sam Evens acting on behalf of the organizers of the summer school on quantization at Notre Dame asked me to give a short series of lectures on geometric quantization. These lectures were meant to prepare a group of graduate mathematics students for talks at the conference on quantization which were to follow the summer school. The notes that follow resulted from this request. They are a mostly faithful record of four one-hour lectures (except lecture 4) plus two appendices: the first one recalls bits and pieces of category theory; the second discusses densities.