Enhanced Quantization: A Primer

TL;DR

This paper introduces an alternative quantization approach that integrates classical and quantum theories, providing new insights and solutions for models that are problematic under traditional methods.

Contribution

It proposes a novel association of classical and quantum quantities, making classical theory a subset of quantum theory, and offers new perspectives on the meaning of quantization.

Findings

Removes singularities in classical solutions

Enables well-defined quantization of certain field models

Provides a unified view of classical and quantum coexistence

Abstract

Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical quantization procedures postulate a direct linking of various c-number and q-number quantities that lie in disjoint realms, along with the quite distinct interpretations given to each realm. In this paper we propose a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory letting them coexist as required. This proposal also shines light on alternative linking assignments of classical and quantum quantities that offer different perspectives on the very meaning of quantization. In this paper we focus on elaborating the general principles, while elsewhere we have published several examples of what this alternative viewpoint can achieve; these examples include removal of singularities in classical solutions to certain models, and an alternative quantization of several field theory models that are trivial when quantized by traditional methods but become well defined and nontrivial when viewed from the new viewpoint.