A Simple Factor in Canonical Quantization yields Affine Quantization Even for Quantum Gravity

TL;DR

This paper compares canonical and affine quantization methods, highlighting how affine quantization's flexibility in operator domains offers advantages for quantum gravity, demonstrated through a straightforward outline.

Contribution

It introduces affine quantization as a simple alternative to canonical quantization, especially useful for quantum gravity applications.

Findings

Affine quantization allows operators with restricted domains.

Affine quantization can be applied to quantum gravity models.

The paper provides a basic outline demonstrating this approach.

Abstract

Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q <\infty$, while the basic AQ operators can fit $-\infty<P<\infty$ and $ 0<Q<\infty$, $-\infty <Q<0$, or even $-\infty<Q\neq0<\infty$. AQ can also be the key to quantum gravity, as our simple outline demonstrates.