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

Symmetry Integrability and Geometry-Methods and Applications

article

Bernd J. Schroers¹  Matthias Wilhelm² 

[1] Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University;Institut für Mathematik und Institut für Physik

关键词: relativistic wave equations;    quantum groups;    curved momentum space;    noncommutative spacetime;   

DOI  :  10.3842/SIGMA.2014.053

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown