Two-dimensional Dirac oscillator in a magnetic field in deformed phase space with minimal-length uncertainty relations
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 495-504 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the dynamics of the Dirac oscillator in a magnetic field. The Heisenberg algebra is constructed in detail in the noncommutative phase space in the presence of minimal length. By means of the Nikiforov–Uvarov method, the energy eigenvalues are obtained exactly and the corresponding wave functions, in momentum space, are expressed in terms of hypergeometric functions.
Keywords: Dirac oscillator, deformed phase space, minimal length, Nikiforov–Uvarov method.
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F. A. Dossa; J. T. Koumagnon; J. V. Hounguevou; G. Y. H. Avossevou. Two-dimensional Dirac oscillator in a magnetic field in deformed phase space with minimal-length uncertainty relations. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 495-504. http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a6/

[1] M. Moreno, A. Zentella, “Covariance, CPT and the Foldy–Wouthuysen transformation for the Dirac oscillator”, J. Phys. A: Math. Gen., 22:17 (1989), L821–L825 | DOI | MR

[2] J. Bentez, R. P. Martínez y Romero, H. N. Núez-Yépez, A. L. Salas-Brito, “Solution and hidden supersymmetry of a Dirac oscillator”, Phys. Rev. Lett., 64:14 (1990), 1643–1645 | DOI | MR

[3] V. I. Kukulin, G. Loyola, M. Moshinsky, “A Dirac equation with an oscillator potential and spin-orbit coupling”, Phys. Lett. A, 158:1–2 (1991), 19–22 | DOI | MR

[4] D. Itô, K. Mori, E. Carriere, “An example of dynamical systems with linear trajectory”, Nuovo Cimento A, 51:4 (1967), 1119–1121 | DOI

[5] M. Moshinsky, A. Szczepaniak, “The Dirac oscillator”, J. Phys. A: Math. Gen., 22:17 (1989), L817–L819 | DOI | MR

[6] M. R. Setare, O. Hatami, “Exact solutions of the Dirac equation for an electron in a magnetic field with shape invariant method”, Chin. Phys. Lett., 25:11 (2008), 3848–3851 | DOI

[7] M. Bednar, J. Ndimubandi, A. G. Nikitin, “On connection between the two-body Dirac oscillator and Kemmer oscillators”, Canadian J. Phys., 75:5 (1997), 283–290 | DOI

[8] C. Quesne, M. Moshinsky, “Symmetry Lie algebra of the Dirac oscillator”, J. Phys. A: Math. Gen., 23:12 (1990), 2263–2272 | DOI | MR

[9] J. Beckers, N. Debergh, “Supersymmetry, Foldy–Wouthuysen transformations, and relativistic oscillators”, Phys. Rev. D, 42:4 (1990), 1255–1259 | DOI | MR

[10] M. Moshinsky, G. Loyola, C. Villegas, “Anomalous basis for representations of the Poincaré group”, J. Math. Phys., 32:2 (1991), 373–381 | DOI | MR

[11] M. Moshinsky, G. Loyola, “Mass spectra of the particle-antiparticle system with a Dirac oscillator interaction”, Workshop on Harmonic Oscillators (University of Maryland, College Park, MD, March 25–28, 1992), NASA Conference Publication Series, 3197, eds. D. Han, Y. S. Kim, W. W.Zachary, NASA, Washington, 1993, 405–421

[12] A. Del Sol Mesa, M. Moshinsky, “Relations between different approaches to the relativistic two-body problem”, J. Phys. A: Math. Gen., 27:13 (1994), 4685–4693 | DOI | MR

[13] J. Beckers, N. Debergh, A. G. Nikitin, “On supersymmetries in nonrelativistic quantum mechanics”, J. Math. Phys., 33:1 (1992), 152–160, arXiv: math-ph/0508021 | DOI | MR

[14] N. Debergh, J. Ndimubandi, D. Strivay, “On relativistic scalar and vector mesons with harmonic oscillatorlike interactions”, Z. Phys. C, 56:3 (1992), 421–425 | DOI

[15] V. V. Dvoeglazov, “The Dirac–Dowker oscillator”, Nouvo Cimento A, 107:9 (1994), 1785–1788, arXiv: hep-th/9404145 | DOI

[16] M. Hosseinpour, H. Hassanabadi, M. de Montigny, “The Dirac oscillator in a spinning cosmic string spacetime”, Eur. Phys. J. C, 79:4 (2019), 311, 7 pp., arXiv: 1904.05889 | DOI

[17] F. A. Dossa, G. Y. H. Avossevou, “Relativistic dynamics for a particle carrying a non-Abelian charge in a non-Abelian background electromagnetic field”, J. Math. Phys., 61:2 (2020), 022302, 13 pp. | DOI | MR

[18] S. Capozziello, G. Lambiase, G. Scarpetta, “Generalized uncertainty principle from quantum geometry”, Internat. J. Theor. Phys., 39:1 (2000), 15–22 | DOI | MR

[19] A. Kempf, G. Mangano, R. B. Mann, “Hilbert space representation of the minimal length uncertainty relation”, Phys. Rev. D, 52:2 (1995), 1108–1118, arXiv: hep-th/9412167 | DOI | MR

[20] L. N. Chang, D. M. Minic, N. Okamura, T. Takeuchi, “Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem”, Phys. Rev. D, 65:12 (2002), 125028, 8 pp., arXiv: hep-th/0201017 | DOI | MR

[21] S. Benczik, L. N. Chang, D. Minic, N. Okamura, S. Rayyan, T. Takeuchi, “Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation”, Phys. Rev. D, 66:2 (2002), 026003, 11 pp., arXiv: hep-th/0204049 | DOI

[22] F. Brau, “Minimal length uncertainty relation and the hydrogen atom”, J. Phys. A: Math. Gen., 32:44 (1999), 7691–7696, arXiv: quant-ph/9905033 | DOI | MR

[23] R. Akhoury, Y.-P. Yao, “Minimal length uncertainty relation and the hydrogen spectrum”, Phys. Lett. B, 572:1–2 (2003), 37–42, arXiv: hep-ph/0302108 | DOI

[24] F. A. Dossa, “One-dimensional harmonic oscillator problem and its hidden $SU(1,1)$ symmetry in the presence of a minimal length”, Phys. Lett. A, 384:35 (2020), 126891, 8 pp. | DOI | MR

[25] F. A. Dossa, “Thermodynamic properties and algebraic solution of the $N$-dimensional harmonic oscillator with minimal length uncertainty relations”, Phys. Scr., 96:10 (2021), 105703, 10 pp. | DOI

[26] K. Nouicer, “An exact solution of the one-dimensional Dirac oscillator in the presence of minimal lengths”, J. Phys. A: Math. Gen., 39:18 (2006), 5125–5134 | DOI | MR

[27] C. Quesne, V. M. Tkachuk, “Dirac oscillator with nonzero minimal uncertainty in position”, J. Phys. A: Math. Gen., 38:8 (2005), 1747–1765, arXiv: math-ph/0412052 | DOI | MR

[28] Z. Selema, A. Boumal, “Two-dimensional boson oscillator under a magnetic field in the presence of a minimal length in the non-commutative space”, Rev. Mex. Fis., 67:2 (2021), 226–237 | DOI

[29] A. F. Nikiforov, V. B. Uvarov, Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1984 | DOI | MR | MR | Zbl

[30] A. Kempf, G. Mangano, “Minimal length uncertainty relation and ultraviolet regularization”, Phys. Rev. D, 55:12 (1997), 7909–7920, arXiv: hep-th/9612084 | DOI

[31] S. Hossenfelder, “A note on theories with a minimal length”, Class. Quantum Grav., 23:5 (2006), 1815–1821, arXiv: hep-th/0510245 | DOI | MR

[32] U. Harbach, S. Hossenfelder, M. Bleicher, H. Stoecker, Signatures of a minimal length scale in high precision experiments, arXiv: hep-ph/0404205

[33] U. Harbach, S. Hossenfelder, “The Casimir effect in the presence of a minimal length”, Phys. Lett. B, 632:2–3 (2006), 379–383, arXiv: hep-th/0502142 | DOI

[34] S. Hossenfelder, “The minimal length and large extra dimensions”, Modern Phys. Lett. A, 19:37 (2006), 2727–2744, arXiv: hep-ph/0410122 | DOI

[35] K. Konishi, G. Paffuti, P. Provero, “Minimum physical length and the generalized uncertainty principle in string theory”, Phys. Lett. B, 234:3 (1990), 276–284 | DOI | MR

[36] E. Sadurní, “The Dirac–Moshinsky oscillator: theory and applications”, AIP Conf. Proc., 1334:1 (2011), 249–290, arXiv: 1101.3011 | DOI

[37] B. Mirza, M. Mohadesi, “The Klein–Gordon and the Dirac oscillators in a noncommutative space”, Commun. Theor. Phys., 42:5 (2004), 664–668 | DOI | MR

[38] A. Boumali, H. Hassanabadi, “The thermal properties of a two-dimensional Dirac oscillator under an external magnetic field”, Eur. Phys. J. Plus, 128:10 (2013), 124, 13 pp. | DOI