We propose a novel class of nonlinear Dirac wave equations in \(3+1\) flat space-time dimensions. Reducing the space dimensions to 2, we study the electron dynamics in an external homogeneous magnetic field for a specific type of one-electron self-interaction providing the possible (nonlinear) ground-state Landau energy levels together with their respective eigenfunctions. We concentrate on the regime of strong magnetic fields and, thus, briefly comment on the relevance of this approach to reveal certain processes thought to occur particularly near the surfaces of magnetars.

中文翻译：

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非线性狄拉克方程和强磁场中的电子动力学

我们在\(3+1\)平面时空维度中提出了一类新的非线性狄拉克波动方程。将空间维度减少到 2，我们研究了外部均匀磁场中特定类型的单电子自相互作用的电子动力学，提供可能的（非线性）基态朗道能级及其各自的本征函数。我们专注于强磁场的范围，因此，简要评论这种方法的相关性，以揭示被认为特别发生在磁星表面附近的某些过程。