Degenerate solutions to the massless Dirac and Weyl equations and a proposed method for controlling the quantum state of Weyl particles

In a recent work we had shown that all solutions to the Weyl equation and a special class of solutions to the Dirac equation are degenerate, in the sense that they remain unaltered under the influence of a wide variety of different electromagnetic fields. In the present article our previous work is extended, providing a wide class of degenerate solutions to the Dirac equation for massless particles. The electromagnetic fields corresponding to these solutions are calculated, giving also some specific examples regarding both spatially constant electromagnetic fields and electromagnetic waves. Further, a general form of solutions to the Weyl equation is presented, and a possible way for fully controlling the state of Weyl particles through appropriate electromagnetic fields is discussed. Finally, the transition from degenerate solutions corresponding to massless particles to non-degenerate solutions corresponding to massive particles is analyzed and it is shown that, under certain conditions, the concept of degeneracy can also be extended, in an approximate sense, to massive particles.