Spin 1/2 particle in the field of the Dirac string on the background of de Sitter space-time

Abstract

The Dirac monopole string is specified for de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of de Sitter space-time in static coordinates. Instead of spinor monopole harmonics, the technique of Wigner D-functions is used. After separation of the variables, detailed analysis of the radial equations is performed; four types of solutions, singular, regular, in- and out- running waves, are constructed in terms of hypergeometric functions. The complete set of spinor wave solutions \Psi_{\epsilon, j,m, \lambda}(t,r, \theta, \phi) has been constructed, special attention is given to treating the states of minimal values of the total angular moment j_{\min}.