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Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
Інший ID:
2010 Mathematics Subject Classification: 83A99; 81R20; 81R50; 81R60
DOI:10.3842/SIGMA.2014.053
DOI:10.3842/SIGMA.2014.053
Посилання:
Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions / B.J. Schroers, M. Wilhelm // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 45 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
full collection is available at http://www.emis.de/journals/SIGMA/space-time.html,
MW thanks the Department of Mathematics at Heriot-Watt University for hospitality during
a six-months visit in 2010 when the bulk of the research reported here was carried out. BJS
thanks Sergio Inglima for discussions and comments on a draft version of the manuscript. Both
MW and BJS thank the University of Ghana for hospitality during a research visit in April
2010.
Дата:
2014
Переглядів:
454
Завантажень:
260
Анотація:
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.
