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The Foldy-Wouthuysen Transformation of the Dirac Equation in Noncommutative Phase-Space
Département de Physique, Faculté des sciences exactes, Université des Frères Mentouri, Constantine, Algeria
Département de Physique, Faculté des sciences exactes, Université des Frères Mentouri, Constantine, Algeria
- 1 Département de Physique, Faculté des sciences exactes, Université des Frères Mentouri, Constantine, Algeria
- 2 Département de Physique, Faculté des sciences exactes, Université des Frères Mentouri, Constantine, Algeria
Journal of Modern Physics·Volume 09 (2018)·Pages 2021–2034·Published 13 September 2018·DOI10.4236/jmp.2018.911127
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Abstract
A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed; in the present work the basic properties of the Dirac hamiltonian in the FW representation in the noncommutative phase-space are investigated and the Schr ö dinger-Pauli equation is found, knowing that the used methods for extracting the full phase-space noncommutative Dirac equation are, the Bopp-shift linear translation method, and the Moyal-Weyl product (*-product).
KeywordsFoldy-Wouthuysen TransformationNonrelativistic LimitNoncommutative Schrödinger-Pauli EquationPhase-Space NoncommutativityNoncommutative Dirac EquationMoyal ProductBopp-Shift Translation
- Foldy, L.L. and Wouthuysen, S.A. (1950) Physical Review, 78, 29. https://doi.org/10.1103/PhysRev.78.29
- Greiner, W. (2000) Quantum Mechanics an Introduction, 4th Edition, Vol. I, Springer, Berlin.
- Greiner, W. (1994) Quantum Mechanics. 3rd Edition, Springer, Berlin, Heidelberg.
- Davydov, A.S. (1965) Quantum Mechanics. 2nd Edition, Pergamon, Oxford.
- Messiah, A. (1968) Quantum Mechanics, Vol. II. Wiley, New York.
- Costello, J.P. and McKellar, B.H.J. (1995) American Journal of Physics, 63, 1119-1121. https://doi.org/10.1119/1.18017
- Silenko, A.J. (2003) Journal of Mathematical Physics, 44, 2952. https://doi.org/10.1063/1.1579991
- Silenko, A.J. (2008) Physical Review A, 77, Article ID: 012116. https://doi.org/10.1103/PhysRevA.77.012116
- Nikitin, A.G. (1998) Journal of Physics A: Mathematical and General, 31, 3297-3300. https://doi.org/10.1088/0305-4470/31/14/015
- Delduc, F., Duret, Q., Gieres, F. and Lefrancois, M. (2008) Journal of Physics Conference Series, 103, Article ID: 012020. https://doi.org/10.1088/1742-6596/103/1/012020
- Douglas, M.R. and Nekrasov, N.A. (2001) Reviews of Modern Physics, 73, 977-1029. https://doi.org/10.1103/RevModPhys.73.977
- Connes, A., Douglas, M.R. and Schwarz, A. (1998) JHEP, 9802, 003. https://doi.org/10.1088/1126-6708/1998/02/003
- Seiberg, N. and Witten, E. (1999) JHEP, 9909, 032. https://doi.org/10.1088/1126-6708/1999/09/032
- Chaichian, M., Demichev, A. and Presnajder, P. (2000) Nuclear Physics B, 567, 360. https://doi.org/10.1016/S0550-3213(99)00664-1
- Mirza, B. and Mohadesi, M. (2014) Communications in Theoretical Physics, 42, 664-668. http://iopscience.iop.org/0253-6102/42/5/664
- Bastos, C., Bertolami, O., Dias, N.C. and Prata, J.N. (2008) Journal of Mathematical Physics, 49, Article ID: 072101. https://doi.org/10.1063/1.2944996
- Eftekharzadeh, A. and Hu, B.L. (2005) Brazilian Journal of Physics, 35, 333-342. https://doi.org/10.1590/S0103-97332005000200019
- Li, K., Wang, J. and Chen, C. (2005) Modern Physics Letters A, 20, 2165-2174. https://doi.org/10.1142/S0217732305017421
- Jiang, X., Long, C. and Qin, S. (2013) Journal of Modern Physics, 4, 940-944. https://www.doi.org/10.4236/jmp.2013.47126