Quantization Methods: A Guide for Physicists and Analysts

TL;DR

This paper provides a comprehensive overview of various quantization techniques used in physics and mathematics, highlighting their successes, limitations, and mathematical structures to aid both specialists and non-specialists.

Contribution

It offers a descriptive, accessible survey of quantization methods, emphasizing their practical applications and mathematical richness for physicists and mathematicians.

Findings

Summarizes key quantization techniques and their applications.

Highlights the successes and shortcomings of each method.

Demonstrates the mathematical structures underlying quantization.

Abstract

In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim to reach both physicists and mathematicians, including non-specialists in the field. It is our hope that an overview such as this will put into perspective the relative successes as well as shortcomings of the various techniques that have been developed and, besides delineating their usefulness in understanding the nature of the quantum regime, will also demonstrate the mathematical richness of the attendant structures.