Eur. Phys. J. Plus (2021) 136: 498
https://doi.org/10.1140/epjp/s13360-021-01502-z

Regular Article

Magnetically confined electrons and the Nambu–Jona-Lasinio model

Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de Los Andes, Santiago, Chile

^a stanleybruces@gmail.com

Received: 26 November 2020
Accepted: 25 April 2021
Published online: 5 May 2021

Abstract

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.