Analytic exact solutions to the nonlinear Dirac equation
arXiv:2604.05750 · doi:10.1088/1402-4896/aea5f9
Abstract
We present analytic exact solutions to the nonlinear Dirac equation: they display a ring singularity for the Nambu--Jona-Lasinio nonlinearity and a shell singularity for the Soler nonlinearity. For both cases, the size of the singular region is of the order of the Compton length. General comments about square-integrability will be addressed in terms of a solution to the linearized system.
arXiv comment8 pages