THE SOLUTIONS OF PAULI EQUATION IN DE SITTER SPACE BACKGROUND AND HOMOGENEOUS MANIFOLD SU(2)=U(1)

Abstract

In this paper, we consider a particle with spin \(\frac{1}{2}\) in de Sitter space-time.  Procedure for transition to the Pauli approximation is conducted in the equation in the variable (t, r), obtained after separating the angular dependence of (ϑ, φ) from the wave function.  We make the suitable second order equation corresponding to de Sitter space time for particle spine \(\frac{1}{2}\) we then compare this equation to Jacobi polynomial and obtain the wave function and eigenvalues (energy spectrum) which is important for the corresponding system.  Also, by taking the advantage from weight and main function in Jacobi polynomial and obtain the corresponding algebra.