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.

中文翻译：

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均匀电场中Dirac振荡器的超对称路径积分

在本文中，我们通过超对称路径积分方法研究二维Dirac振荡器与均匀电场之间的相互作用，其中根据Fradkin和Gitman协变量模型，用奇数源表示描述自旋自由度的费米离子变量。精确计算了传播子，并推导了能量特征值及其特征旋转。此外，通过使用传播器的各种对称特性，我们以允许我们直接以归一化形式获得特征自旋子的方式来表示它。还研究了该问题的非相对论极限和电流密度。