Abstract
A simple example of classical physics may be defined as classical variables, p and q, and quantum physics may be defined as quantum operators, P and Q. The classical world of , as it is currently understood, is truly disconnected from the quantum world, as it is currently understood. The process of quantization, for which there are several procedures, aims to promote a classical issue into a related quantum issue. In order to retain their physical connection, it becomes critical as to how to promote specific classical variables to associated specific quantum variables. This paper, which also serves as a review paper, leads the reader toward specific, but natural, procedures that promise to ensure that the classical and quantum choices are guaranteed a proper physical connection. Moreover, parallel procedures for fields, and even gravity, that connect classical and quantum physical regimes, will be introduced.
Highlights
This project is a review of several of the author’s articles, which feature several important consequences that apply to ‘Quantum Mechanics and Its Foundations’
Since affine quantization (AQ) is not designed to deal with a full-harmonic oscillator, we immediately admit that AQ fails on the full-harmonic oscillator, and we examine using AQ for a halfharmonic oscillator
Conventional wave functions are ψ(x) and joining two wave functions leads to φ∗(x) ψ(x) dx. We reviewed this procedure for canonical quantization (CQ) because AQ has a different procedure
Summary
This project is a review of several of the author’s articles, which feature several important consequences that apply to ‘Quantum Mechanics and Its Foundations’. We begin by establishing unique classical and quantum tools that preserve the physical role, i.e., beyond merely the mathematical role, of the necessary variables in each realm. This will include the traditional canonical quantization (CQ) tools, as well as spin quantization (SQ) tools (which are not considered much further), and as well as (relatively new) tools referred to as affine quantization (AQ) tools. These reliable tools are used to examine various models, which run from harmonic oscillators, to field theory, to Einstein’s gravity, and well beyond. While those topics are covered in this work, we need to start by introducing our tools
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