Completing Canonical Quantization, and its Role in Nontrivial Scalar Field Quantization

TL;DR

This paper redefines canonical quantization to allow classical and quantum theories to coexist for >0, enabling new quantization methods for scalar fields like _n across various spacetime dimensions.

Contribution

It introduces a modified canonical quantization framework that supports nontrivial scalar field quantization in multiple dimensions, expanding the scope of quantum field theory.

Findings

Supports conventional quantization procedures

Reveals new quantization methods for scalar fields

Enables nontrivial _n scalar field quantization in all  or more dimensions

Abstract

The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization procedures that, among several examples, permit nontrivial quantization of scalar field models such as \phi^4_n, for every spacetime dimension n\ge2.