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

TL;DR

This paper provides exact solutions for particles with spins 0, 1/2, and 1 in de Sitter space, showing that the reflection coefficient vanishes under certain conditions, indicating no potential barrier for these particles.

Contribution

It introduces explicit solutions for various spins in de Sitter space and demonstrates that the reflection coefficient is zero when specific quantum number constraints are met, challenging previous assumptions.

Findings

Reflection coefficient R_{εj} vanishes under certain conditions.

No potential barrier exists in the effective potential for these particles.

Exact solutions for scalar, electromagnetic, and Dirac fields are provided.

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 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.