The secret to fixing incorrect canonical quantizations

Covariant scalar field quantizations will be called (φr)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 where r < 2n/(n − 2) can be treated by canonical quantization, while models where r > 2n/(n−2) are trivial or, if treated as a unit, emerge as ‘free theories’. Moreover, according to canonical quantization, models where r = 2n/(n−2), e.g., r = n = 4, also become ‘free theories’, which must be considered quantum failures. However, there exists a different approach called affine quantization. This approach promotes a different set of classical variables to become the basic quantum operators and offers different results. It is well known that the canonical quantization of φ44 fails. This article addresses this failure alongside solutions to other problems.

Authors

Institutions

Publication Details

Journal
Academia quantum.
Published
2024-10-14
DOI
https://doi.org/10.20935/acadquant7349
Citations
3
Primary Topic
Computability, Logic, AI Algorithms
Type
article
Field-Weighted Citation Impact
1.08
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

The secret to fixing incorrect canonical quantizations

Riccardo Fantoni, John R. Klauder
3 citations
Academia quantum.
Computability, Logic, AI Algorithms
1.08
article

The secret to fixing incorrect canonical quantizations

Riccardo Fantoni, John R. Klauder
article en
3 citations

Abstract

Covariant scalar field quantizations will be called (φr)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 where r < 2n/(n − 2) can be treated by canonical quantization, while models where r > 2n/(n−2) are trivial or, if treated as a unit, emerge as ‘free theories’. Moreover, according to canonical quantization, models where r = 2n/(n−2), e.g., r = n = 4, also become ‘free theories’, which must be considered quantum failures. However, there exists a different approach called affine quantization. This approach promotes a different set of classical variables to become the basic quantum operators and offers different results. It is well known that the canonical quantization of φ44 fails. This article addresses this failure alongside solutions to other problems.

Academia quantum.Vol. 1(1)
University of Trieste (IT), University of Florida (US)
Openalex Percentile: Top 20%
Computability, Logic, AI Algorithms
1.08
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

The secret to fixing incorrect canonical quantizations — Riccardo Fantoni, John R. Klauder · Academia quantum. (2024) | TGRS Research Map | TGRS