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

TL;DR

This paper extends the understanding of degenerate solutions to the massless Dirac and Weyl equations, explores electromagnetic field configurations, and proposes a method to control Weyl particle quantum states via electromagnetic fields.

Contribution

It introduces a broad class of degenerate solutions for the massless Dirac equation and a control method for Weyl particle states using electromagnetic fields.

Findings

Derived new degenerate solutions for massless Dirac particles.

Calculated electromagnetic fields corresponding to these solutions.

Proposed a method for controlling Weyl particle quantum states.

Abstract

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.