Preprint 2014-02
Bernd J. Schroers, Matthias Wilhelm
Towards non-commutative deformations of relativistic wave equations in 2+1 dimensions.
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.
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-02
MSC 2000:
23 pp.