Version 1
: Received: 16 July 2024 / Approved: 17 July 2024 / Online: 17 July 2024 (09:17:24 CEST)
Version 2
: Received: 12 September 2024 / Approved: 13 September 2024 / Online: 13 September 2024 (10:41:17 CEST)
How to cite:
Klauder, J.; Fantoni, R. The Secret to Fixing Incorrect Canonical Quantizations. Preprints2024, 2024071397. https://doi.org/10.20944/preprints202407.1397.v2
Klauder, J.; Fantoni, R. The Secret to Fixing Incorrect Canonical Quantizations. Preprints 2024, 2024071397. https://doi.org/10.20944/preprints202407.1397.v2
Klauder, J.; Fantoni, R. The Secret to Fixing Incorrect Canonical Quantizations. Preprints2024, 2024071397. https://doi.org/10.20944/preprints202407.1397.v2
APA Style
Klauder, J., & Fantoni, R. (2024). The Secret to Fixing Incorrect Canonical Quantizations. Preprints. https://doi.org/10.20944/preprints202407.1397.v2
Chicago/Turabian Style
Klauder, J. and Riccardo Fantoni. 2024 "The Secret to Fixing Incorrect Canonical Quantizations" Preprints. https://doi.org/10.20944/preprints202407.1397.v2
Abstract
Covariant scalar field quantization, nicknamed $(\vp^r)_n$, where $r$ denotes the power of the interaction term and $n=s+1$ where $s$ is the spatial dimension and $1$ adds time.Models such that $r<2n/(n-2)$ can be treated by canonical quantization, while models such that$r>2n/(n-2)$ are trivial, or, if treated as a unit,emerge as `free theories'. Models such as $r=2n/(n-2)$, e.g., $r=n=4$, again using canonical quantization also become `free theories', which must be considered quantum failures. However, there exists a different approach called affinequantization that promotes a different set of classical variables to become the basic quantum operators and it offers different results. It is well-known that the canonical quantization of $\varphi^4_4$ fails. Here is how to fix it along with many other problems.
Keywords
canonical quantization; affine quantization; field theory
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
