Prequantization, geometric quantization, corrected geometric quantization

TL;DR

This paper reviews and compares key aspects of geometric quantization of symplectic manifolds, discussing criticisms, facts, and improvements to the theory, serving as an accessible introduction for newcomers.

Contribution

It provides a comparative overview and critical analysis of geometric quantization, highlighting recent improvements and clarifying fundamental concepts.

Findings

Identifies limitations and criticisms of existing geometric quantization methods

Proposes improvements to the theory of geometric quantization

Summarizes key points and developments in the field

Abstract

A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the "salient points of the theory". The unfamiliar reader can consider this as a "soft" introduction to the topic.