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We show that the $(2+1)$-dimensional Dirac-Moshinsky oscillator coupled to anexternal magnetic field can be treated algebraically with the $SU(1,1)$ grouptheory and its group basis. We use the $su(1,1)$ irreducible representationtheory to find the energy spectrum and the eigenfunctions. Also, with the$su(1,1)$ group basis we construct the relativistic coherent states in a closedform for this problem.

Coherent states for the two-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field