We investigate the planar nonlinear quantum dynamics of a self-interacting electron in the presence of an external homogeneous magnetic field in \(3+1\) flat space-time dimensions. In cylindrical coordinates, nonlinearities are introduced via the Nambu–Jona-Lasinio interaction. Special attention is given to the strong-field QED regime. We obtain the approximate (nonlinear) ground-state Landau energy levels together with their respective eigenfunctions. We briefly comment on the relevance of this model to elucidate certain processes thought to occur near the surfaces of neutron stars.

中文翻译：

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磁约束电子和Nambu–Jona-Lasinio模型

我们研究在（3 + 1 \）平面时空尺寸中存在外部均匀磁场的情况下，自相互作用电子的平面非线性量子动力学。在圆柱坐标系中，非线性是通过Nambu-Jona-Lasinio相互作用引入的。特别关注强场QED制度。我们获得了近似的（非线性）基态朗道能级以及它们各自的本征函数。我们简要评论该模型的相关性，以阐明某些被认为发生在中子星表面附近的过程。