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Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Towards {Non-Commutative} {Deformations} of {Relativistic} {Wave} {Equations} in 2+1 {Dimensions}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a52/}
}
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Bernd J. Schroers; Matthias Wilhelm. Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a52/

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