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

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.