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

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

2010-01-25

arxiv.org/abs/1001.4415v2

Ricerche di matematica, 2011, Vol. 60, no. 1, P. 57-88

Physics

High Energy Physics

High Energy Physics - Theory

30 pages. This paper is an updated and more comprehensive version of the old paper V.M. Red'kov. On Particle penetrating throu

Scientific paper

10.1007/s11587-010-0096-3

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 a 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 >> j, where \rho 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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