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arXiv · 1402.7039

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

Bernd J. Schroers·Matthias Wilhelm
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Abstract

We consider the deformation of the Poincar\'e 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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Bernd J. Schroers, Matthias Wilhelm. 2014-02-27. Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions. https://doi.org/10.3842/sigma.2014.053

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