Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
We consider the deformation of the Poincaré group in 2+1 dimensions into the quantum double of the Lorentz group and construct Lorentz-covariant momentum-space formulations of the irreducible representations describing massive particles with spin 0, 1/2 and 1 in the deformed theory. We discuss ways...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146686 |
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| Zitieren: | Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions / B.J. Schroers, M. Wilhelm // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 45 назв. — англ. |
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Schroers, B.J. Wilhelm, M. 2019-02-10T18:14:08Z 2019-02-10T18:14:08Z 2014 Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions / B.J. Schroers, M. Wilhelm // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 45 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83A99; 81R20; 81R50; 81R60 DOI:10.3842/SIGMA.2014.053 https://nasplib.isofts.kiev.ua/handle/123456789/146686 We consider the deformation of the Poincaré group in 2+1 dimensions into the quantum double of the Lorentz group and construct Lorentz-covariant momentum-space formulations of the irreducible representations describing massive particles with spin 0, 1/2 and 1 in the deformed theory. We discuss ways of obtaining non-commutative versions of relativistic wave equations like the Klein-Gordon, Dirac and Proca equations in 2+1 dimensions by applying a suitably defined Fourier transform, and point out the relation between non-commutative Dirac equations and the exponentiated Dirac operator considered by Atiyah and Moore. This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The full collection is available at http://www.emis.de/journals/SIGMA/space-time.html, MW thanks the Department of Mathematics at Heriot-Watt University for hospitality during a six-months visit in 2010 when the bulk of the research reported here was carried out. BJS thanks Sergio Inglima for discussions and comments on a draft version of the manuscript. Both MW and BJS thank the University of Ghana for hospitality during a research visit in April 2010. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions |
| spellingShingle |
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions Schroers, B.J. Wilhelm, M. |
| title_short |
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions |
| title_full |
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions |
| title_fullStr |
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions |
| title_full_unstemmed |
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions |
| title_sort |
towards non-commutative deformations of relativistic wave equations in 2+1 dimensions |
| author |
Schroers, B.J. Wilhelm, M. |
| author_facet |
Schroers, B.J. Wilhelm, M. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We consider the deformation of the Poincaré group in 2+1 dimensions into the quantum double of the Lorentz group and construct Lorentz-covariant momentum-space formulations of the irreducible representations describing massive particles with spin 0, 1/2 and 1 in the deformed theory. We discuss ways of obtaining non-commutative versions of relativistic wave equations like the Klein-Gordon, Dirac and Proca equations in 2+1 dimensions by applying a suitably defined Fourier transform, and point out the relation between non-commutative Dirac equations and the exponentiated Dirac operator considered by Atiyah and Moore.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146686 |
| citation_txt |
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions / B.J. Schroers, M. Wilhelm // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 45 назв. — англ. |
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AT schroersbj towardsnoncommutativedeformationsofrelativisticwaveequationsin21dimensions AT wilhelmm towardsnoncommutativedeformationsofrelativisticwaveequationsin21dimensions |
| first_indexed |
2025-11-30T17:43:04Z |
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2025-11-30T17:43:04Z |
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1850858331811348480 |