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, 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.
| Original language | English |
|---|---|
| Journal | Symmetry, Integrability and Geometry: Methods and Applications |
| Volume | 10 |
| Pages (from-to) | 053 |
| ISSN | 1815-0659 |
| DOIs | |
| Publication status | Published - 20 May 2014 |
| Externally published | Yes |