Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space

We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant classification of the forty-five orthogonal separabl...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2022
Main Authors: Valero, Carlos, McLenaghan, Raymond G.
Format: Article
Language:English
Published: Інститут математики НАН України 2022
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211526
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space. Carlos Valero and Raymond G. Mclenaghan. SIGMA 18 (2022), 019, 28 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Valero, Carlos
McLenaghan, Raymond G.
author_facet Valero, Carlos
McLenaghan, Raymond G.
citation_txt Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space. Carlos Valero and Raymond G. Mclenaghan. SIGMA 18 (2022), 019, 28 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant classification of the forty-five orthogonal separable webs modulo the action of the isometry group. The eighty-eight inequivalent coordinate charts adapted to the webs are also determined and listed. We find a number of separable webs that do not appear in previous works in the literature. Further, the method used seems to be more efficient and concise than those employed in earlier works.
first_indexed 2026-03-16T12:21:30Z
format Article
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id nasplib_isofts_kiev_ua-123456789-211526
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-16T12:21:30Z
publishDate 2022
publisher Інститут математики НАН України
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spelling Valero, Carlos
McLenaghan, Raymond G.
2026-01-05T12:25:23Z
2022
Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space. Carlos Valero and Raymond G. Mclenaghan. SIGMA 18 (2022), 019, 28 pages
1815-0659
2020 Mathematics Subject Classification: 53Z05; 70H20; 83A05
arXiv:1805.12228
https://nasplib.isofts.kiev.ua/handle/123456789/211526
https://doi.org/10.3842/SIGMA.2022.019
We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant classification of the forty-five orthogonal separable webs modulo the action of the isometry group. The eighty-eight inequivalent coordinate charts adapted to the webs are also determined and listed. We find a number of separable webs that do not appear in previous works in the literature. Further, the method used seems to be more efficient and concise than those employed in earlier works.
The authors wish to thank K. Rajaratnam and the anonymous referees for their careful reading of the paper and a number of helpful suggestions and comments. We also wish to acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada in the form of an Undergraduate Student Research Award (CV) and a Discovery Grant (RGM).
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
Article
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spellingShingle Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
Valero, Carlos
McLenaghan, Raymond G.
title Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
title_full Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
title_fullStr Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
title_full_unstemmed Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
title_short Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
title_sort classification of the orthogonal separable webs for the hamilton-jacobi and klein-gordon equations on 3-dimensional minkowski space
url https://nasplib.isofts.kiev.ua/handle/123456789/211526
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AT mclenaghanraymondg classificationoftheorthogonalseparablewebsforthehamiltonjacobiandkleingordonequationson3dimensionalminkowskispace