  In a recent work, we have 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 this study, our previous work is significantly
extended, providing a wide class of degenerate solutions to the Dirac equation
for massless particles. The electromagnetic fields corresponding to these
solutions are calculated and examples regarding both spatially constant
electromagnetic fields and electromagnetic waves are also provided.
Furthermore, some general solutions to the Weyl equation are presented, and the
corresponding electromagnetic fields are calculated. Based on these results, a
method for fully controlling the quantum state of Weyl particles using
appropriate electromagnetic fields is proposed. Finally, the transition from
degenerate to non-degenerate solutions as the particles acquire mass is
discussed.
