The Doublet of Dirac Particles in a Non-Abelian Monopole Field: Pauli Approximation

Abstract

The paper studies the general Pauli-like equation for a Dirac fermions doublet on the background of an external non-Abelian monopole field. The variables separation has been fulfilled, the non-relativistic approximation for the radial systems has been derived. For the case of a minimal value of the conserved quantum number j = 0, the Pauli equation has been obtained in the form of one second-order differential equation. In the case j > 0, the problem has been reduced to the system of two coupled second order equations. In Bogomol’nyi–Prasad–Sommerfeld approximation, this system of equations has been solved in terms of hypergeometric functions.