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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862635369224208384 |
|---|---|
| author | Schroers, B.J. Wilhelm, M. |
| author_facet | Schroers, B.J. Wilhelm, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-30T17:43:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146686 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T17:43:04Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions Schroers, B.J. Wilhelm, M. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146686 |
| work_keys_str_mv | AT schroersbj towardsnoncommutativedeformationsofrelativisticwaveequationsin21dimensions AT wilhelmm towardsnoncommutativedeformationsofrelativisticwaveequationsin21dimensions |