Spin 1/2 Particle in the Field of the Dirac String on the background of Anti de Sitter Space-Time

TL;DR

This paper investigates the behavior of a spin 1/2 particle in an anti de Sitter space-time influenced by a Dirac monopole string, providing exact solutions and analyzing the energy spectrum.

Contribution

It introduces a new method using Wigner D-functions to solve the Dirac equation in this context and constructs the complete set of solutions.

Findings

Energy spectrum is discrete for all quantum numbers.

Exact solutions are expressed in hypergeometric functions.

Special focus on states with minimal total angular momentum.

Abstract

The Dirac monopole string is specified for anti de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of anti 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 radial equations have been solved exactly in terms of hypergeometric functions. The complete set of spinor wave solutions has been constructed, the most attention is given to treating the states of minimal values for total moment quantum number j_{min}. At all values of j, the energy spectrum is discrete.