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We study the relativistic bound state dynamics of electrons in the presence of electromagnetic fields within the framework of a novel class of nonlinear Dirac wave equations. In 2 + 1 space–time dimensions, we address a specific interacting electron model in a homogeneous magnetic field providing the allowed nonlinear ground-state Landau energy levels. We concentrate on the regime of laboratory high magnetic fields, and thus, comment on the relevance of this approach to study 2D electron systems.

Relativistic electron dynamics in magnetic fields with low-degree of field nonlinearity