The Favored Classical Variables to Promote to Quantum Operators

TL;DR

This paper explores how selecting the appropriate classical variables for quantization is crucial for accurately solving quantum systems, with examples from scalar fields and gravity highlighting the importance of variable choice.

Contribution

It introduces a method to identify favored classical variables that lead to valid quantizations of complex systems like scalar fields and gravity.

Findings

Choosing the right classical variables improves quantization accuracy.

Variable selection impacts the analysis of non-renormalizable fields.

Proper variable promotion aids in solving quantum gravity problems.

Abstract

Classical phase-space variables are normally chosen to promote to quantum operators in order to quantize a given classical system. While classical variables can exploit coordinate transformations to address the same problem, only one set of quantum operators to address the same problem can give the correct analysis. Such a choice leads to the need to find the favored classical variables in order to achieve a valid quantization. This article addresses the task of how such favored variables are found that can be used to properly solve a given quantum system. Examples, such as non-renormalizable scalar fields and gravity, have profited by initially changing which classical variables to promote to quantum operators.