English

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

General Relativity and Quantum Cosmology 2021-08-10 v1 Quantum Physics

Abstract

Canonical quantization (CQ) is built around [Q,P]=i1 ⁣ ⁣1[Q,P]=i\hbar1\!\!1, while affine quantization (AQ) is built around [Q,D]=iQ[Q,D]=i\hbar\,Q, where D(PQ+QP)/2D\equiv(PQ+QP)/2. The basic CQ operators must fit <P,Q<-\infty< P, Q <\infty, while the basic AQ operators can fit <P<-\infty<P<\infty and 0<Q< 0<Q<\infty, <Q<0-\infty <Q<0, or even <Q0<-\infty<Q\neq0<\infty. AQ can also be the key to quantum gravity, as our simple outline demonstrates.

Keywords

Cite

@article{arxiv.2108.04083,
  title  = {A Simple Factor in Canonical Quantization yields Affine Quantization Even for Quantum Gravity},
  author = {John R. Klauder},
  journal= {arXiv preprint arXiv:2108.04083},
  year   = {2021}
}

Comments

6 pages; a simple introduction to affine quantization that even helps quantum gravity

R2 v1 2026-06-24T04:57:12.659Z