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

Harvard

Schroers, BJ & Wilhelm, M 2014, 'Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions', Symmetry, Integrability and Geometry: Methods and Applications, vol. 10, pp. 053. https://doi.org/10.3842/SIGMA.2014.053

APA

Schroers, B. J., & Wilhelm, M. (2014). Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions. Symmetry, Integrability and Geometry: Methods and Applications, 10, 053. https://doi.org/10.3842/SIGMA.2014.053

Vancouver

Schroers BJ, Wilhelm M. Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions. Symmetry, Integrability and Geometry: Methods and Applications. 2014 Jan 1;10:053. https://doi.org/10.3842/SIGMA.2014.053

Author

Schroers, Bernd J. ; Wilhelm, Matthias. / Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions. In: Symmetry, Integrability and Geometry: Methods and Applications. 2014 ; Vol. 10. pp. 053.

Bibtex

@article{3d99bc988965486cb950cb7fcef4fed1,
title = "Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions",
abstract = " 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. ",
keywords = "hep-th, gr-qc, math-ph, math.MP",
author = "Schroers, {Bernd J.} and Matthias Wilhelm",
year = "2014",
month = jan,
day = "1",
doi = "10.3842/SIGMA.2014.053",
language = "English",
volume = "10",
pages = "053",
journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",
issn = "1815-0659",
publisher = "Natsional'na Akademiya Nauk Ukrainy Instytut Matematyky",

}

RIS

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