On Solutions of the Pauli Equation in Non-Static De Sitter Metrics

Abstract

A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit the existence of the non-relativistic limit in the covariant Dirac equation. Procedure for transition to the Pauli approximation is conducted in the equations in the variables (t, r), obtained after separating the angular dependence of (θ, ϕ) from the wave function. The non-relativistic systems of equations in the variables (t, r) is solved exactly in both models. The constructed wave functions do not represent stationary states with fixed energy, however the corresponding probability density does not depend on the time.