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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 053, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.053 (Mi sigma918) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions

Bernd J. Schroersa, Matthias Wilhelmb

a Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
b Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS-Adlershof, Zum Großen Windkanal 6, 12489 Berlin, Germany
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DOI: https://doi.org/10.3842/SIGMA.2014.053
URL: https://www.emis.de/journals/SIGMA/2014/053/
Abstract: 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, $\frac12$ 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.
Keywords: relativistic wave equations; quantum groups; curved momentum space; non-commutative spacetime.
Received: February 28, 2014; in final form May 9, 2014; Published online May 20, 2014
Bibliographic databases:
Document Type: Article
MSC: 83A99; 81R20; 81R50; 81R60
Language: English
Citation: Bernd J. Schroers, Matthias Wilhelm, “Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions”, SIGMA, 10 (2014), 053, 23 pp.
Citation in format AMSBIB
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\by Bernd~J.~Schroers, Matthias~Wilhelm
\paper Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
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\papernumber 053
\totalpages 23
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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