On solutions of the Pauli equations in not static de Sitter metrics

Mozyr State Pedagogical University named after I.P. Shamyakin, Belarus

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 existence of the non-relativistic limit in the covariant Dirac equation. Procedure for transition to the Pauli approximation is conducted in the systems of the four equations in the variables $(t, r)$, obtained after separating the angular dependence of $(\theta, \phi)$ in 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.