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
Datum:2014
Hauptverfasser: Schroers, B.J., Wilhelm, M.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2014
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146686
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146686
record_format dspace
spelling 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
institution 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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first_indexed 2025-11-30T17:43:04Z
last_indexed 2025-11-30T17:43:04Z
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