Dirac spinor solitons or bags

Abstract

Explicit solutions of a non-linear Dirac equation in the four-dimensional Minkowski space have been found. They are continuous eigenfunctions of spin 1 2 , energy and parity, and are confined to the interior of a sphere of definite radius a, with no tails outside the sphere. They are called solitons in the paper though the name of spinor droplets or bags may be more appropriate. Because of the Lorentz covariance of the Dirac equations, arbitrarily moving solitons can be obtained from the rest system solutions by applying proper Lorentz transformations.