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In a recent work, we have shown that all solutions to the Weyl equation and aspecial class of solutions to the Dirac equation are degenerate in the sensethat they remain unaltered under the influence of a wide variety of differentelectromagnetic fields. In this study, our previous work is significantlyextended, providing a wide class of degenerate solutions to the Dirac equationfor massless particles. The electromagnetic fields corresponding to thesesolutions are calculated and examples regarding both spatially constantelectromagnetic fields and electromagnetic waves are also provided.Furthermore, some general solutions to the Weyl equation are presented, and thecorresponding electromagnetic fields are calculated. Based on these results, amethod for fully controlling the quantum state of Weyl particles usingappropriate electromagnetic fields is proposed. Finally, the transition fromdegenerate to non-degenerate solutions as the particles acquire mass isdiscussed.

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