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 › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Article number	053
Journal	Symmetry, Integrability and Geometry: Methods and Applications
Volume	10
DOIs	https://doi.org/10.3842/SIGMA.2014.053
Publication status	Published - 20 May 2014

Keywords

Curved momentum space
Non-commutative spacetime
Quantum groups
Relativistic wave equations

ASJC Scopus subject areas

Analysis
Geometry and Topology
Mathematical Physics

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10.3842/SIGMA.2014.053

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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 = "Curved momentum space, Non-commutative spacetime, Quantum groups, Relativistic wave equations",

author = "Schroers, {Bernd J.} and Matthias Wilhelm",

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language = "English",

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AU - Schroers, Bernd J.

AU - Wilhelm, Matthias

PY - 2014/5/20

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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 - Curved momentum space

KW - Non-commutative spacetime

KW - Quantum groups

KW - Relativistic wave equations

U2 - 10.3842/SIGMA.2014.053

DO - 10.3842/SIGMA.2014.053

M3 - Article

AN - SCOPUS:84901198865

SN - 1815-0659

VL - 10

JO - Symmetry, Integrability and Geometry: Methods and Applications

JF - Symmetry, Integrability and Geometry: Methods and Applications

M1 - 053

ER -

Towards non-commutative deformations of relativistic wave equations in 2+1 dimensions

Abstract

Keywords

ASJC Scopus subject areas

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