Localized degenerate solutions to the massless Dirac and Weyl equations

Abstract

In this article we present a general class of localized degenerate solutions to the massless Dirac and Weyl equations, which can also describe particles, or systems of particles, with varying energy and spin along their direction of motion. Another interesting characteristic of these solutions is that they remain unaltered in a wide range of electromagnetic 4-potentials and fields, which are analytically calculated. In addition, we propose a new method for spatially separating Weyl particles based on their helicity and direction of motion using appropriate magnetic fields, given in explicit form.