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arXiv · 2108.04083

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

John R. Klauder
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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.

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John R. Klauder. 2021-08-06. A Simple Factor in Canonical Quantization yields Affine Quantization Even for Quantum Gravity. https://arxiv.org/abs/2108.04083

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