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

Bernd J. Schroers; Matthias Wilhelm

doi:10.3842/SIGMA.2014.053

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

Bernd J. Schroers, Matthias Wilhelm

Research output: Contribution to journal › Journal article › Research › peer-review

5 Citations (Scopus)

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.

Original language	English
Journal	Symmetry, Integrability and Geometry: Methods and Applications
Volume	10
Pages (from-to)	053
ISSN	1815-0659
DOIs	https://doi.org/10.3842/SIGMA.2014.053
Publication status	Published - 1 Jan 2014
Externally published	Yes

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10.3842/SIGMA.2014.053

Cite this

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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",

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

AU - Schroers, Bernd J.

AU - Wilhelm, Matthias

PY - 2014/1/1

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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 -