Nonlinear Phenomena in Complex Systems, 2022, Vol.25, No.2, pp.136

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2022, Vol.25, No. 2, pp.136 - 158

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

E. M. Ovsiyuk, N. G. Krylova, V. Balan, and V. M. Red'kov

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.

Key words: quantum mechanics, Dirac particle, non-Abelian monopole field

DOI: https://doi.org/10.33581/1561-4085-2022-25-2-136-158

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