Heun-type solutions for the Dirac particle on the curved background of Minkowski space-times

• URL: http://arxiv.org/abs/2308.10518v1
• Date: Mon, 21 Aug 2023 07:11:25 GMT
• Title: Heun-type solutions for the Dirac particle on the curved background of Minkowski space-times
• Authors: Saman Rahmani and Hossein Panahi and Amerne Najafizade
• Abstract summary: We study the Dirac equation in the background of Minkowski space-time on a light cone. Results are valid for a spinless charged particle in the context of the magnetic field.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: In the present paper, we study the Dirac equation in the background of Minkowski space-time on a light cone. With the help of the coupling of the radial parts, the system of 4 equations is reduced to two different second-order differential equations, which coincide with a particle in present potentials. It turns out that the central equation reduces to Heun-type equations and provides us with energy spectra. Also, it is shown that the Schr\"odinger equation like with a combination of the external field is related to a second-order differential equation. In another way to solve the problem, results are valid for a spinless charged particle in the context of the magnetic field. Keywords: Heun function, Dirac equation, curved space-time, light cone

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