Soluble extensions of the Dirac oscillator with exact and broken supersymmetry

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Abstract
We consider a large class of Dirac oscillator-type couplings that exhibit a three-dimensional hidden supersymmetry. A subclass of exactly soluble cases is determined by using the Infeld and Hull procedure. We find that the corresponding spectra possess a high degree of unphysical degeneracy, similar to the Dirac oscillator case. This difficulty is overcome by proposing a further generalization of this coupling, which breaks supersymmetry but retains exact solubility. We also discuss the covariance properties of the new coupling together with its Poincaré-invariant extension to the many-particle case.