Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
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Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions. / Schroers, Bernd J.; Wilhelm, Matthias.
In: Symmetry, Integrability and Geometry: Methods and Applications, Vol. 10, 01.01.2014, p. 053.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
AU - Schroers, Bernd J.
AU - Wilhelm, Matthias
PY - 2014/1/1
Y1 - 2014/1/1
N2 - 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.
AB - 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.
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
VL - 10
SP - 053
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
ER -
ID: 227488929