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Year 2022, , 132 - 136, 30.03.2022

Evrim Ersin Kangal

https://doi.org/10.17776/csj.1052798

Abstract

References

  • [1] Nyambuya G. G., General Spin Dirac Equation (II), Journal of Modern Physics, 4 (2013) 1050-1058.
  • [2] Tokmehdashi H., Rajabi A.A., Hamzavi M., Dirac Equation with Mixed Scalar–Vector–Pseudoscalar Linear Potential under Relativistic Symmetries, Zeitschrift für Naturforschung A, 70 (2015) 713-720.
  • [3] Rubinow S. I., Joseph B. K., Asymptotic Solution of the Dirac Equation, Phys. Rev., 87 (1963) 2789-2796.
  • [4] Thaller B., The Dirac Equation, Texts and Monographs in Physics. 1nd ed. Berlin, (1992).
  • [5] Hassanabadi H., Zare S., Montigny, M., Relativistic spin-zero bosons in a Som–Raychaudhuri space–time, Gen. Relat. Grav., 50 (2018) 104-129.
  • [6] Mozaffari F.S., Hassanabadi H., Sobhani H., Chung J., Investigation of the Dirac Equation by Using the Conformable Fractional Derivative, Korean Phys. Soc., 72 (2018) 987-990. [7] Sargolzaeipor S., Hassanabadi H., Chung W.S., Superstatistics of the Klein–Gordon equation in deformed formalism for modified Dirac delta distribution, Mod. Phys. Lett. A, 33 (2018) 1850060-1850071.
  • [8] Sogut K., Salti M., Aydogdu O., Quantum dynamics of the photon in rainbow gravity, Annals of Physics, 431 (2021) 168556-168566.
  • [9] Bakke K., Mota H., Aharonov–Bohm effect for bound states in the cosmic string spacetime in the context of rainbow gravity, General Relativity, and Gravitation, 52 (2020) 52-67. [10] Junior E.L.B., Rodrigues M.E., Regular black holes in Rainbow Gravity, Nuclear Physics B, 961 (2020) 15244-15258.
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  • [12] Lobo I.P., Christian P., Reaching the Planck scale with muon lifetime measurements, Phys. Rev. D, 103, (2021) 106025-106033.
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  • [14] Giovanni A.C., Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale, International Journal of Modern Physics D, 11 (2002) 35-59.
  • [15] Leiva C., Saavedra J., Villanueva J., Geodesic structure of the schwarzschild black hole in rainbow gravity, Modern Physics Letters A, 24(2009) 1443-1451.
  • [16] Giovanni A.C., Phenomenology of doubly special relativity, International Journal of Modern Physics A, 20 (2005) 6007-6037.
  • [17] Magueijo J., Smolin L., Generalized Lorentz invariance with an invariant energy scale, Physical Review D, 67 (2003) 044017-044029.
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  • [19] Magueijo J., Smolin L., Gravity's rainbow, Class. Quant. Grav., 21(2004) 1725–1736.
  • [20] Feng Z.W., Yan S.Z., Thermodynamic phase transition of a black hole in rainbow gravity, Phys. Lett. B, 772(2017) 737-742.
  • [21] Villalba V.M., Greiner W., Creation of scalar and Dirac particles in the presence of a time varying electric field in an anisotropic Bianchi type I universe, Physical Review D, 65(2001) 025007- 025013.
  • [22] Pauli W., Handbuch der Physik, 24 (1933).
  • [23]Sakurai J.J., Advanced Quantum Mechanics. 1nd ed. USA, (1967).
  • [24]Gurtler R., Hestenes D., Observables, operators, and complex numbers in the Dirac theory, J. Math. Phys., 16 (1974) 556-572.
  • [25]Dirac P. A. M., The quantum theory of the electron, Proceedings of the Royal Society of London A, 117 (1928) 610-626.
  • [26]Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, (1964).
  • [27] Tiwari S.,C., Gordon decomposition of Dirac current: a new interpretation, arXiv:1206.3643, 2017.
  • [28]W. Gordon,Über den Stoß zweier Punktladungen nach der Wellenmechanik, Z.Phys., 48(1928) 180–191.

Dynamics of the Dirac Particle in an Anisotropic Rainbow Universe

Year 2022, , 132 - 136, 30.03.2022

Evrim Ersin Kangal

https://doi.org/10.17776/csj.1052798

Abstract

An alternative way of understanding physical effects in curved space time is to solve the associated particle equation such as the Dirac equation. It is a first-order relativistic wave equation and defines spin-1/2 massive particles like electrons and quarks. In this study, we solved the Dirac equation in an anisotropic rainbow universe. Subsequently, the reduced wave equation is obtained by making use of the asymptotic property of the Whittaker function. In the final stage, we calculate each component of the spin current density and then graphically evaluate their behavior according to the rainbow function. According to our results, the spin current density only depends on the z component of the momentum. In addition, the sign of both spin current densities is not changing with time. Finally, the current density amplitude in the high energy state or high scale parameter
(ϵ=0.9) is rapidly decreasing faster than in ϵ=0.6 and ϵ=0.3.

Keywords

Dirac Equation Rainbow Function Spin Current Density

References

  • [1] Nyambuya G. G., General Spin Dirac Equation (II), Journal of Modern Physics, 4 (2013) 1050-1058.
  • [2] Tokmehdashi H., Rajabi A.A., Hamzavi M., Dirac Equation with Mixed Scalar–Vector–Pseudoscalar Linear Potential under Relativistic Symmetries, Zeitschrift für Naturforschung A, 70 (2015) 713-720.
  • [3] Rubinow S. I., Joseph B. K., Asymptotic Solution of the Dirac Equation, Phys. Rev., 87 (1963) 2789-2796.
  • [4] Thaller B., The Dirac Equation, Texts and Monographs in Physics. 1nd ed. Berlin, (1992).
  • [5] Hassanabadi H., Zare S., Montigny, M., Relativistic spin-zero bosons in a Som–Raychaudhuri space–time, Gen. Relat. Grav., 50 (2018) 104-129.
  • [6] Mozaffari F.S., Hassanabadi H., Sobhani H., Chung J., Investigation of the Dirac Equation by Using the Conformable Fractional Derivative, Korean Phys. Soc., 72 (2018) 987-990. [7] Sargolzaeipor S., Hassanabadi H., Chung W.S., Superstatistics of the Klein–Gordon equation in deformed formalism for modified Dirac delta distribution, Mod. Phys. Lett. A, 33 (2018) 1850060-1850071.
  • [8] Sogut K., Salti M., Aydogdu O., Quantum dynamics of the photon in rainbow gravity, Annals of Physics, 431 (2021) 168556-168566.
  • [9] Bakke K., Mota H., Aharonov–Bohm effect for bound states in the cosmic string spacetime in the context of rainbow gravity, General Relativity, and Gravitation, 52 (2020) 52-67. [10] Junior E.L.B., Rodrigues M.E., Regular black holes in Rainbow Gravity, Nuclear Physics B, 961 (2020) 15244-15258.
  • [11] Ling Y., Song H., Hongbao Z., The Kinematics of Particles Moving in Rainbow Spacetime, Modern Physics Letters A, 22 (2007) 2931–2938.
  • [12] Lobo I.P., Christian P., Reaching the Planck scale with muon lifetime measurements, Phys. Rev. D, 103, (2021) 106025-106033.
  • [13] Giovanni A.C., Testable scenario for relativity with minimum length, Physics Letter B, 510 (2001) 255-263.
  • [14] Giovanni A.C., Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale, International Journal of Modern Physics D, 11 (2002) 35-59.
  • [15] Leiva C., Saavedra J., Villanueva J., Geodesic structure of the schwarzschild black hole in rainbow gravity, Modern Physics Letters A, 24(2009) 1443-1451.
  • [16] Giovanni A.C., Phenomenology of doubly special relativity, International Journal of Modern Physics A, 20 (2005) 6007-6037.
  • [17] Magueijo J., Smolin L., Generalized Lorentz invariance with an invariant energy scale, Physical Review D, 67 (2003) 044017-044029.
  • [18] Kimberly D., Magueijo J., Medeiros, J., Nonlinear relativity in position space, Physical Review D, 70 (2004) 084007- 084014.
  • [19] Magueijo J., Smolin L., Gravity's rainbow, Class. Quant. Grav., 21(2004) 1725–1736.
  • [20] Feng Z.W., Yan S.Z., Thermodynamic phase transition of a black hole in rainbow gravity, Phys. Lett. B, 772(2017) 737-742.
  • [21] Villalba V.M., Greiner W., Creation of scalar and Dirac particles in the presence of a time varying electric field in an anisotropic Bianchi type I universe, Physical Review D, 65(2001) 025007- 025013.
  • [22] Pauli W., Handbuch der Physik, 24 (1933).
  • [23]Sakurai J.J., Advanced Quantum Mechanics. 1nd ed. USA, (1967).
  • [24]Gurtler R., Hestenes D., Observables, operators, and complex numbers in the Dirac theory, J. Math. Phys., 16 (1974) 556-572.
  • [25]Dirac P. A. M., The quantum theory of the electron, Proceedings of the Royal Society of London A, 117 (1928) 610-626.
  • [26]Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, (1964).
  • [27] Tiwari S.,C., Gordon decomposition of Dirac current: a new interpretation, arXiv:1206.3643, 2017.
  • [28]W. Gordon,Über den Stoß zweier Punktladungen nach der Wellenmechanik, Z.Phys., 48(1928) 180–191.
There are 26 citations in total.

Details

Primary Language English
Subjects Classical Physics (Other)
Journal Section Natural Sciences
Authors

Evrim Ersin Kangal 0000-0001-5906-3143

Publication Date March 30, 2022
Submission Date January 3, 2022
Acceptance Date February 24, 2022
Published in Issue Year 2022

Cite

APA Kangal, E. E. (2022). Dynamics of the Dirac Particle in an Anisotropic Rainbow Universe. Cumhuriyet Science Journal, 43(1), 132-136. https://doi.org/10.17776/csj.1052798