Nonlinear Dirac equations and the electron dynamics in strong magnetic fields
Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de Los Andes, Santiago, Chile
Accepted: 12 July 2021
Published online: 27 July 2021
We propose a novel class of nonlinear Dirac wave equations in 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021