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.
Originalsprog | Engelsk |
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Tidsskrift | Symmetry, Integrability and Geometry: Methods and Applications |
Vol/bind | 10 |
Sider (fra-til) | 053 |
ISSN | 1815-0659 |
DOI | |
Status | Udgivet - 1 jan. 2014 |
Udgivet eksternt | Ja |
Emneord
- hep-th
- gr-qc
- math-ph
- math.MP