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 Rie-mann, 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.
Keywords: doublet of fermions, non-Abelian monopole, Pauli approximation, spaces of constant curvature, bound states.
Å.Ì. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University
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À.N. Red'ko – M. Tank Belarusian State Pedagogical University, Minsk
V.V. Kisel – Belarusian State University of Informatics and Radioelectronics, Minsk
V.Ì. Red'kov – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk