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The SO(4,1) gauge-invariant theory of the Dirac fermions in the externalfield of the Kaluza-Klein monopole is investigated. It is shown that thediscrete quantum modes are governed by reducible representations of the o(4)dynamical algebra generated by the components of the angular momentum operatorand those of the Runge-Lenz operator of the Dirac theory in Taub-NUTbackground. The consequence is that there exist central and axial discretemodes whose spinors have no separated variables.Comment: 17 pages, latex, no figures. Version to appear in Class.Quantum Gra

Dynamical algebra and Dirac quantum modes in the Taub-NUT background