Abstract
•A soluble covariant generalization of the two-dimensional Dirac oscillator, with a supersymmetry breaking, is considered.•The energy eigenvalues and eigenstates of the system are obtained using chiral creation and annihilation operators.•The effect of the coupling to an external uniform transverse magnetic field on the dynamics of the system is studied.•The connection with Jaynes-Cummings and Anti-Jaynes-Cummings models of quantum optics is discussed.
We consider a soluble covariant extension of the two-dimensional Dirac oscillator (2D DO), which breaks the infinite degeneracy of the energy spectrum. The energy eigenvalues and the corresponding eigenstates of the system are obtained algebraically using chiral creation and annihilation operators. The effect of the coupling to an external constant transverse magnetic field is investigated. The connection with Jaynes-Cummings (JC) and Anti-Jaynes-Cummings (AJC) models of quantum optics, and other features of the system are also discussed.