How to Secure Valid Quantizations

TL;DR

This paper discusses criteria for selecting appropriate classical variables to ensure valid quantization in quantum mechanics, preventing incorrect physical interpretations.

Contribution

It provides a framework for identifying unique variables and their quantum operators to guarantee valid quantizations across particles, fields, and gravity.

Findings

Criteria for selecting classical variables for quantization

Guidelines to avoid invalid quantizations

Application to particles, fields, and gravity

Abstract

Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will outline how the favored variables and their suitable quantum operators is guaranteed to assure a truly valid quantization. Invalid quantizations may be mistaken for valid ones, which then leads to incorrect physics. Besides particle examples, there is also a brief run-through for fields and gravity.