Research ArticleNo Access

Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

Department of Physics, Faculty of Sciences, Salman Farsi University of Kazerun, Kazerun 73175-457, Iran

E-mail Address: b_khosropour@kazerunsfu.ac.ir

https://doi.org/10.1142/S0219887821501991Cited by:3 (Source: Crossref)

Abstract

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

Keywords:

PACS: 03.65.pm, 04.60.−m, 04.60.Bc

References

1. F. Scardigli , Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment, Phys. Lett. B 452 (1999) 39. Crossref, Web of Science, Google Scholar
2. M. Maggiore , Quantum groups, gravity, and the generalized uncertainty principle, Phys. Rev. D 49 (1994) 5182. Crossref, Web of Science, Google Scholar
3. L. J. Garay , Quantum gravity and minimum length, Int. J. Mod. Phys. A 10 (1995) 145. Link, Web of Science, Google Scholar
4. S. Hossenfelder, M. Bleicher, S. Hofmann, J. Ruppert, S. Scherer and H. Stoecker , Signatures in the Planck regime, Phys. Lett. B 575 (2003) 85. Crossref, Web of Science, Google Scholar
5. C. Bambi and F. R. Urban , Classical and quantum gravity natural extension of the generalized uncertainty principle, Class. Quantum Grav. 25 (2008) 095006. Crossref, Web of Science, Google Scholar
6. M. Maggiore , A generalized uncertainty principle in quantum gravity, Phys. Lett. B 304 (1993) 65. Crossref, Web of Science, Google Scholar
7. S. Das and E. C. Vagenas , Universality of quantum gravity corrections, Phys. Rev. Lett. 101 (2008) 221301. Crossref, Web of Science, Google Scholar
8. M. Khalil , Some implications of two forms of the generalized uncertainty principle, Adv. High Energy Phys. 2014 (2014) 619498. Crossref, Web of Science, Google Scholar
9. S. K. Moayedi, M. R. Setare, H. Moayeri and M. Poorakbar , Formulation of the spinor field in the presence of a minimal length based on the Quesne–Tkachuk algebra, Int. J. Mod. Phys. A 26 (2011) 4981. Link, Web of Science, Google Scholar
10. S. Das and E. C. Vagenas , Phenomenological implications of the generalized uncertainty principle, Can. J. Phys. 87 (2009) 233. Crossref, Web of Science, Google Scholar
11. P. Pedram , New approach to nonperturbative quantum mechanics with minimal length uncertainty, Phys. Rev. D 85 (2012) 024016. Crossref, Web of Science, Google Scholar
12. K. Nouricer , Casimir effect in the presence of minimal lengths, J. Phys. A 38 (2005) 10027. Crossref, Google Scholar
13. B. Khosropour , The generalized uncertainty principle and the Stark effect, Acta Phys. Polon. B 48 (2017) 217. Crossref, Web of Science, Google Scholar
14. A. F. Ali, S. Das and E. C. Vagenas , Discreteness of space from the generalized uncertainty principle, Phys. Lett. B 678 (2009) 497. Crossref, Web of Science, Google Scholar
15. S. Das, E. C. Vagenas and A. F. Ali , Discreteness of space from GUP II: Relativistic wave equations, Phys. Lett. B 690 (2010) 407. Crossref, Web of Science, Google Scholar
16. K. Nozari, V. Hosseinzadeh and M. A. Gorji , High temperature dimensional reduction in Snyder space, Phys. Lett. B 750 (2015) 218. Crossref, Web of Science, Google Scholar
17. S. K. Moayedi, M. R. Setare and B. Khosropour , Lagrangian formulation of a magnetostatic field in the presence of a minimal length scale based on the Kempf algebra, Int. J. Mod. Phys. A 28 (2013) 1350142. Link, Web of Science, Google Scholar
18. T. V. Fityo , Statistical physics in deformed spaces with minimal length, Phys. Lett. A 372 (2008) 587. Crossref, Web of Science, Google Scholar
19. 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 (2016) 247. Crossref, Web of Science, Google Scholar
20. K. Nozari and P. Pedram , Minimal length and bouncing-particle spectrum, Eur. Phys. Lett. 92 (2010) 50013. Crossref, Web of Science, Google Scholar
21. S. Benczik et al., Hydrogen-atom spectrum under a minimal-length hypothesis, Phys. Rev. A 72 (2005) 012104. Crossref, Web of Science, Google Scholar
22. C. Quesne and V. M. Tkachuk , Lorentz-covariant deformed algebra with minimal length and application to the $(1 + 1)$ -dimensional Dirac oscillator, J. Phys. A: Math. Gen. 39 (2006) 10909. Crossref, Web of Science, Google Scholar
23. C. Quesne and V. M. Tkachuk , Lorentz-covariant deformed algebra with minimal length, Czech. J. Phys. 56 (2006) 1269. Crossref, Web of Science, Google Scholar
24. F. Brau , Minimal length uncertainty relation and the hydrogen atom, J. Phys. A: Math. Gen. 32 (1999) 7691. Crossref, Google Scholar
25. W. Greiner , Relativistic Quantum Mechanics: Wave Equations, 3rd edn. (Springer-Verlag, Berlin, 2000). Crossref, Google Scholar
26. D. Griffiths , Introduction to Elementary Particles (John Wiley Sons, 1987). Crossref, Google Scholar
27. A. Bzdak and V. Skokov , Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions, Phys. Lett. B 710 (2012) 171. Crossref, Web of Science, Google Scholar
28. K. Konishi, G. Paffuti and P. Provero , Minimum physical length and the generalized uncertainty principle in string theory, Phys. Lett. B 234 (1990) 276. Crossref, Web of Science, Google Scholar
29. S. Capozziello, G. Lambiase and G. Scarpetta , Generalized uncertainty principle from quantum geometry, Int. J. Theor. Phys. 39 (2000) 15. Crossref, Web of Science, Google Scholar
30. T. Kanazawa, G. Lambiase, G. Vilasi and A. Yoshioka , Noncommutative Schwarzschild geometry and generalized uncertainty principle, Eur. Phys. J. C 79 (2019) 95. Crossref, Web of Science, Google Scholar
31. D. Amati, M. Ciafaloni and G. Veneziano , Classical and quantum gravity effects from Planckian energy superstring collisions, Int. J. Mod. Phys. A 3 (1988) 615. Link, Web of Science, Google Scholar