Geodesic
Plasma oscillations in a generalized Snyder space
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 378-388 Cet article a éte moissonné depuis la source Math-Net.Ru

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Since Snyder was the first to present the theory of quantized space–time, many studies have been devoted to various phenomenological aspects of this theory. In this paper, we investigate the plasma frequency in a generalized Snyder space. The electron and ion plasma waves in a generalized Snyder space are found. We estimate the upper bound on the isotropic minimal length scale, which is close to $l_0\sim 10^{-9}$ m.
Keywords: phenomenology of quantum gravity, generalized uncertainty principle, minimal length, plasma frequency.
Mots-clés : plasma oscillations 
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B. Khosropour. Plasma oscillations in a generalized Snyder space. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 378-388. http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a9/

[1] H. S. Snyder, “Quantized space-time”, Phys. Rev., 71:1 (1947), 38–41 | DOI | MR

[2] G. Amelino-Camelia, F. Giacomini, G. Gubitosi, “Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes”, Phys. Lett. B, 784 (2018), 50–55, arXiv: 1805.09363 | DOI

[3] Kh. P. Gnatenko, V. M. Tkachuk, “Macroscopic body in the Snyder space and minimal length estimation”, Europhys. Lett., 125:5 (2019), 50003, 5 pp., arXiv: 1901.10811 | DOI

[4] N. Seiberg, E. Witten, “String theory and noncommutative geometry”, JHEP, 09 (1999), 032, 93 pp. | DOI | MR

[5] S. Mignemi, “Classical and quantum mechanics of the nonrelativistic Snyder model”, Phys. Rev. D, 84:2 (2011), 025021, 11 pp., arXiv: 1104.0490 | DOI

[6] K. Fredenhagen, F. Reszewski, “Polymer state approximation of Schrödinger wavefunctions”, Class. Quantum Grav., 23:22 (2006), 6577–6584, arXiv: gr-qc/0606090 | DOI | MR

[7] M. V. Battisti, S. Meljanac, “Scalar field theory on noncommutative Snyder spacetime”, Phys. Rev. D, 82:2 (2010), 024028, 9 pp., arXiv: 1003.2108 | DOI | MR

[8] F. Girelli, E. R. Livine, “Scalar field theory in Snyder space-time: alternatives”, JHEP, 03 (2011), 132, 31 pp. | DOI | MR

[9] G. Jaroszkiewicz, “A dynamical model for the origin of Snyder's quantized spacetime algebra”, J. Phys. A: Math. Gen., 28:12 (1995), L343–L348 | DOI | MR

[10] R. Banerjee, S. Kulkarni, S. Samanta, “Deformed symmetry in Snyder space and relativistic particle dynamics”, JHEP, 05 (2006), 077, 22 pp. | DOI

[11] L. J. Garay, “Quantum gravity and minimum length”, Internat. J. Modern Phys. A, 10:2 (1995), 145–166, arXiv: gr-qc/9403008 | DOI

[12] L. Lu, A. Stern, “Particle dynamics on Snyder space”, Nucl. Phys. B, 860:1 (2012), 186–205, arXiv: 1110.4112 | DOI | MR

[13] S. Mignemi, “Classical and quantum mechanics of the nonrelativistic Snyder model in curved space”, Class. Quantum Grav., 29:21 (2012), 215019, 19 pp. | DOI | MR

[14] C. Leiva, “Harmonic oscillator in Snyder space: the classical case and the quantum case”, Pramana J. Phys., 74:2 (2010), 169–175, arXiv: 0809.0066 | DOI

[15] L. Tonks, I. Langmuir, “Oscillations in ionized gases”, Phys. Rev., 33:2 (1929), 195–210 | DOI

[16] A. Kempf, “Non-pointlike particles in harmonic oscillators”, J. Phys. A: Math. Gen., 30:6 (1997), 2093–2101, arXiv: hep-th/9604045 | DOI | MR

[17] 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

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

[19] M. M. Stetsko, V. M. Tkachuk, “Perturbation hydrogen-atom spectrum in deformed space with minimal length”, Phys. Rev. A, 74:1 (2006), 012101, 5 pp., arXiv: quant-ph/0603042 | DOI

[20] 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

[21] M. Sprenger, P. Nicolini, M. Bleicher, “Physics on the smallest scales: an introduction to minimal length phenomenology”, Eur. J. Phys., 33:4 (2012), 853–862 | DOI

[22] S. K. Moayedi, M. R. Setare, B. Khosropour, “Lagrangian formulation of a magnetostatic field in the presence of a minimal length scale based on the Kempf algebra”, Internat. J. Modern Phys. A, 28:30 (2013), 1350142, 15 pp., arXiv: 1306.1070 | DOI | MR

[23] B. Khosropour, “Radiation and generalized uncertainty principle”, Phys. Lett. B, 785 (2018), 3–8 | DOI | MR

[24] B. Khosropour, “Angular momentum and Zeeman effect in the presence of a minimal length based on the Kempf–Mann–Mangano algebra”, Eur. Phys. J. Plus, 131:7 (2016), 247, 8 pp. | DOI

[25] B. Khosropour, M. Eghbali, S. Ghorbanali, “$q$-nonlinear Schrodinger and $q$-nonlinear Klein–Gordon equations in the frame work of GUP”, Gen. Rel. Grav., 50:3 (2018), 25, 9 pp. | DOI | MR

[26] M. Faizal, “Consequences of deformation of the Heisenberg algebra”, Internat. J. Geom. Meth. Modern Phys., 12:2 (2015), 1550022, 9 pp., arXiv: 1404.5024 | DOI | MR

[27] Y. Chargui, L. Chetouani, A. Trabelsi, “Exact solution of $D$-dimensional Klein–Gordon oscillator with minimal length”, Commun. Theor. Phys., 53:2 (2010), 231–236 | DOI

[28] F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, Plenum, New York, 2016 | DOI

[29] K. S. Thorne, R. D. Blandford, Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics, Princeton Univ. Press, Princeton, NJ, 2017 | MR

[30] T. G. Pavlopoulos, “Breakdown of Lorentz invariance”, Phys. Rev., 159:5 (1967), 1106–1110 | DOI

[31] W. Heisenberg, “Zur Quantentheorie der Elementarteilchen”, Z. Naturforschung, 5:5 (1950), 251–259 | DOI | MR

[32] W. Heisenberg, “Über die in der Theorie der Elementarteilchen auftretende universelle Länge”, Ann. Phys., 32 (1938), 20–33 | DOI

[33] Kh. Nouicer, “Casimir effect in the presence of minimal lengths”, J. Phys. A: Math. Gen., 38:46 (2005), 10027–10035 | DOI | MR