Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
High Energy Physics - Theory
2014-05-21 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1402.7039,
title = {Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions},
author = {Bernd J. Schroers and Matthias Wilhelm},
journal= {arXiv preprint arXiv:1402.7039},
year = {2014}
}