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

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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.
TidsskriftSymmetry, Integrability and Geometry: Methods and Applications
Sider (fra-til)053
StatusUdgivet - 1 jan. 2014
Eksternt udgivetJa


  • hep-th, gr-qc, math-ph, math.MP

ID: 227488929