Isotopic doublet of the Dirac particles in presence of the non-Abelian monopole: the Pauli approximation

For the doublet of Dirac particles in presence of external non-Abelian fields, a non-relativistic Pauli equation is constructed. It is detailed for the case of the Bogomolny–Prasad–Sommerfeld monopole potentials. The problem of existence of bound states in the system is studied. Comparison of the behavior of the Dirac particles doublet in three spaces of constant curvature: Euclid, Lobachevsky, and Riemann, is performed, from where it follows that the known nonsingular monopole solution usually used for the case of Minkowski space is the application of a mathematical possibility more naturally related to the Lobachevsky space model. Within that treatment, in all three space models, no bound states for the doublet of fermions in the non-Abelian monopole potential exist.