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On exact solutions for quantum particles with spin S = 0, 1/2, 1 and de Sitter event horizon

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Abstract

Exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space–time model are examined in detail. Firstly, for scalar particle, two pairs of linearly independent solutions are specified explicitly: running and standing waves. A known algorithm for calculation of the reflection coefficient \({R_{\epsilon j}}\) on the background of the de Sitter space–time model is analyzed. It is shown that the determination of \({R_{\epsilon j}}\) requires an additional constrain on quantum numbers \({\epsilon \rho / \hbar c \gg j}\), where ρ is a curvature radius. When taken into account of this condition, the \({R_{\epsilon j}}\) vanishes identically. It is claimed that the calculation of the reflection coefficient \({R_{\epsilon j}}\) is not required at all because there is no barrier in an effective potential curve on the background of the de Sitter space–time. The same conclusion holds for arbitrary particles with higher spins, it is demonstrated explicitly with the help of exact solutions for electromagnetic and Dirac fields.

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Red’kov, V.M., Ovsiyuk, E.M. On exact solutions for quantum particles with spin S = 0, 1/2, 1 and de Sitter event horizon. Ricerche mat. 60, 57–88 (2011). https://doi.org/10.1007/s11587-010-0096-3

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