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

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.

arXiv commentIn this version we have corrected a mistake regarding the calculation of the electromagnetic fields from the electromagnetic 4-potentials. The physical interpretation of the results does not change

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Cited by in corpus (6)

• On the remarkable properties of Weyl particles
• A general method for obtaining degenerate solutions to the Dirac and Weyl equations and a discussion on the experimental detection of degenerate states
• Degenerate solutions to the Dirac equation for massive particles and their applications in quantum tunneling
• A novel device for controlling the flow of information based on Weyl fermions and some interesting remarks regarding the electromagnetic interactions of high energy particles
• Localized degenerate solutions to the massless Dirac and Weyl equations
• Degenerate wave-like solutions to the Dirac equation for massive particles