Notes on Geometric Quantization

TL;DR

This paper provides an introductory overview of geometric quantization, covering its mathematical foundations and connections to classical and quantum mechanics, with exercises and examples for better understanding.

Contribution

It offers a comprehensive introduction to geometric quantization, including key mathematical concepts and practical examples, for students and researchers.

Findings

Clarifies the mathematical background of geometric quantization

Provides detailed examples and exercises for learning

Connects geometric quantization with classical and quantum mechanics

Abstract

These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable manifolds, symplectic manifolds and the geometry of line bundles and connections. Moreover, these notes are endowed with several exercises and examples.