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

TY - JOUR

T1 - Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions

AU - Schroers, Bernd J.

AU - Wilhelm, Matthias

PY - 2014/5/20

Y1 - 2014/5/20

N2 - 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.

AB - 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.

KW - hep-th

KW - gr-qc

KW - math-ph

KW - math.MP

U2 - 10.3842/sigma.2014.053

DO - 10.3842/sigma.2014.053

M3 - Journal article

SN - 1815-0659

VL - 10

SP - 053

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

ER -