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, inand out- running waves, are constructed in terms of hypergeometric functions. The complete set of spinor wave solutions ( ) j m t r            has been constructed, special attention is given to treating the states of minimal values of the total angular moment min j . Key words: Dirac monopole string, de Sitter space-time, Dirac equation, Wigner Dfunction, hypergeometric function.