全部 标题 作者
关键词 摘要


The Phase-Space Noncommutativity Effect on the Large and Small Wave-Function Components Approach at Dirac Equation

DOI: 10.4236/oalib.1104108, PP. 1-10

Subject Areas: Applied Physics, Modern Physics, Quantum Mechanics, Theoretical Physics, Mathematical Analysis

Keywords: Schrodinger-Pauli Equation, Noncommutative Nonrelativistic Limit, Noncommutativity of Phase-Space, Noncommutative Dirac Equation, Moyal Product, Bopp-Shift Transformation

Full-Text   Cite this paper   Add to My Lib

Abstract

By the large and small wave-function components approach we achieved the nonrelativistic limit of the Dirac equation in interaction with an electromagnetic potential in noncommutative phase-space, and we tested the effect of the phase-space noncommutativity on it, knowing that the nonrelativistic limit of the Dirac equation gives the Schrodinger-Pauli equation.

Cite this paper

Haouam, I. (2018). The Phase-Space Noncommutativity Effect on the Large and Small Wave-Function Components Approach at Dirac Equation. Open Access Library Journal, 5, e4108. doi: http://dx.doi.org/10.4236/oalib.1104108.

References

[1]  Snyder, H.S. (1946) Quantized Space-Time. Physical Review, 71, 38.
https://doi.org/10.1103/PhysRev.71.38
[2]  Yang, C.N. (1947) On Quantized Space-Time. Physical Review, 72, 874.
https://doi.org/10.1103/PhysRev.72.874
[3]  Banks, T., Fischler, W., Shenker, S. and Susskind, L. (1997) M Theory as a Matrix Model: A Conjecture. Physical Review D, 55, 5112.
https://doi.org/10.1103/PhysRevD.55.5112
[4]  Douglas, M.R. and Nekrasov, N.A. (2001) Noncommutative Field Theory. Reviews of Modern Physics, 73, 977-1029.
https://doi.org/10.1103/RevModPhys.73.977
[5]  Connes, A., Douglas, M.R. and Schwarz, A. (1998) Noncommutative Geometry and Matrix Theory. Journal of High Energy Physics, 9802, 003.
https://doi.org/10.1088/1126-6708/1998/02/003
[6]  Seiberg, N. and Witten, E. (1999) String Theory and Noncommutative Geometry. Journal of High Energy Physics, 9909, 032.
https://doi.org/10.1088/1126-6708/1999/09/032
[7]  Chaichian, M., Demichev, A. and Presnajder, P. (2000) Quantum Field Theory on Non-Commutative Space-Times and the Persistence of Ultraviolet Divergences. Nuclear Physics B, 567, 360.
https://doi.org/10.1016/S0550-3213(99)00664-1
[8]  Duffin, R.J. (1938) On the Characteristic Matrices of Covariant Systems. Physical Review, 54, 1114.
https://doi.org/10.1103/PhysRev.54.1114
[9]  Kemmer, N. (1938) Quantum Theory of Einstein-Bose Particles and Nuclear Interaction. Proceedings of the Royal Society A, 166, 127.
https://doi.org/10.1098/rspa.1938.0084
[10]  Kemmer, N. (1939) The Particle Aspect of Meson Theory. Proceedings of the Royal Society A, 173, 91.
https://doi.org/10.1098/rspa.1939.0131
[11]  Foldy, L. and Wouthuysen, S. (1950) On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit. Physical Review, 78, 29.
[12]  Nikitin, A.G. (1998) On Exact Foldy-Wouthuysen Transformation. Journal of Physics A: Mathematical and General, 31, 3297-3300.
https://doi.org/10.1088/0305-4470/31/14/015
[13]  Jansen, G. and Hess, B.A. (1989) Revision of the Douglas-Kroll Transformation. Physical Review A, 39, 6016-6017.
https://doi.org/10.1103/PhysRevA.39.6016
[14]  Reiher, M. (2006) Douglas-Kroll-Hess Theory: A Relativistic Electrons-Only Theory for Chemistry. Theoretical Chemistry Accounts, 116, 241-252.
[15]  Nakajima, T. (2012) The Douglas-Kroll-Hess Approach. Chemical Reviews, 112, 385-402.
https://doi.org/10.1021/cr200040s
[16]  Greiner, W. (1994) Quantum Mechanics. 3rd Edition, Springer, Berlin, Heidelberg.
[17]  Bechouche, P., Mauser, N. and Bechouche, P. (1998) (Semi)-Nonrelativistic Limits of the Dirac Equation with External Time-Dependent Electromagnetic Field. Communications in Mathematical Physics, 197, 405-425.
https://doi.org/10.1007/s002200050457
[18]  Bjorken, J.D. and Drell, S.D. (1964) Relativistic Quantum Mechanics. McGraw-Hill, New York.
[19]  Davydov, A.S. (1965) Quantum Mechanics. 2nd Edition, Pergamon, Oxford, 63.
[20]  Messiah, A. (1968) Quantum Mechanics, Vol. II. Wiley, New York, 4. V.B.
[21]  Berestetskii, V.B., Lifshitz, E.M. and Pitaevskii, L.P. (1989) Quantum Electrodynamics. 2nd Edition, Pergamon, Oxford.
[22]  Jiang, X., Long, C. and Qin, S. (2013) Solution of Dirac Equation with the Time-Dependent Linear Potential in Non-Commutative Phase. Journal of Modern Physics, 4, 940-944.
https://doi.org/10.4236/jmp.2013.47126
[23]  Hassenabadi, H., Molaee, Z. and Zarrinkamar, S. (2014) Noncommutative Phase Space Schrodinger Equation with Minimal Length. Advances in High Energy Physics, 2014, Article ID: 459345.
[24]  Mirza, B. and Mohadesi, M. (2014) The Klein-Gordon and the Dirac Oscillators in a Noncom-Mutative Space. Theor. Phys. Communications in Theoretical Physics, 42, 664-668.
[25]  Hua, W.J. and Kang, L. (2007) He-McKellar-Wilkens Effect in Noncommutative Space. Chinese Physics Letters, 24, 5.
https://doi.org/10.1088/0256-307X/24/1/002
[26]  Kupriyanov, V.G. (2013) Hydrogen Atom on Curved Noncommutative Space. Journal of Physics A, 46, Article ID: 245303.
https://doi.org/10.1088/1751-8113/46/24/245303
[27]  Adorno, T.C., Baldiotti, M.C., Chaichian, M., Gitman, D.M. and Tureanu, A. (2009) Dirac Equation in Noncommutative Space for Hydrogen Atom. Physics Letters B, 682, 235.
https://doi.org/10.1016/j.physletb.2009.11.003
[28]  Bertolamia, O. and Queirozb, R. (2011) Phase-Space Noncommutativity and the Dirac Equation. Physics Letters A, 375, 4116-4119.
https://doi.org/10.1016/j.physleta.2011.09.053
[29]  Gosselin, P., Bérard, A. and Mohrbach, H. (2006) Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections. The European Physical Journal B, 58, 137-148.
https://doi.org/10.1140/epjb/e2007-00212-6
[30]  Nowakowski, M. (1999) The Quantum Mechanical Current of the Pauli Equation. American Journal of Physics, 67, 916.
https://doi.org/10.1119/1.19149
[31]  Torres del Castillo, G.F. and Velázquez Castro, J. (2004) Schrodinger-Pauli Equation for Spin-3/2 Particles. Revistamexicana de física, 50, 306-310.
[32]  Hestenes, D. (1990) The Zitterbewegung Interpretation of Quantum Mechanics. Foundations of Physics, 20, 1213-1232.
https://doi.org/10.1007/BF01889466
[33]  Huang, K. (1952) On the Zitterbewegung of the Dirac Electron. American Journal of Physics, 20, 479.
https://doi.org/10.1119/1.1933296

Full-Text


comments powered by Disqus