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

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.