Revisiting Canonical Quantization

TL;DR

This paper proposes a new approach to canonical quantization that naturally embeds classical theory within quantum theory for 4>04, offering improved results in some cases compared to traditional methods.

Contribution

It introduces an alternative association between classical and quantum quantities that better reflects the physical reality of 4>04 and enhances quantization outcomes.

Findings

New quantization procedure aligns classical and quantum theories more naturally.

Some examples show improved results over conventional quantization.

Maintains the successful aspects of traditional methods.

Abstract

Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory with \hbar>0, in conformity with the real world wherein nature has chosen \hbar>0 rather than \hbar=0. While keeping the good results of conventional procedures, some examples are presented for which the new procedures offer better results than conventional ones.