Supersymmetric path integral for the Dirac oscillator in a uniform electric field

In this paper, we study the interaction between the two-dimensional Dirac oscillator and a uniform electric field via the supersymmetric path integrals method where the fermionic variables that describe the spin degrees of freedom are expressed by odd sources according to the Fradkin and Gitman covariant model. The propagator is calculated exactly and the energy eigenvalues as well as their eigenspinors are deduced. Moreover, by using various symmetry properties of the propagator, we represented it in a way that allowed us to obtain the eigenspinors directly in normalized form. The nonrelativistic limit and the density of current for this problem are also studied. (paper)