Towards non-commutative deformations of relativistic wave equations in 2+1 dimensions

Bernd J. Schroers, Matthias Wilhelm

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 languageEnglish
Article number053
JournalSymmetry, Integrability and Geometry: Methods and Applications
Publication statusPublished - 20 May 2014


  • Curved momentum space
  • Non-commutative spacetime
  • Quantum groups
  • Relativistic wave equations

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics


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