This article is cited in 5 papers

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

Bernd J. Schroers^a, Matthias Wilhelm<sup>b

a</sup> 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

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.

MSC: 83A99; 81R20; 81R50; 81R60

Received: February 28, 2014; in final form May 9, 2014; Published online May 20, 2014

Language: English

DOI: 10.3842/SIGMA.2014.053

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ArXiv: 1402.7039