Degenerate wave-like solutions to the Dirac equation for massive particles

¹ Department of Physics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens - GR-15772 Zografou Athens, Greece
² Department of Physics, University of Thessaly - GR-35100 Lamia, Greece
³ Department of Computer Science and Biomedical Informatics, University of Thessaly - GR-35131 Lamia, Greece

^(a) E-mail: gtsig@mail.ntua.gr (corresponding author)

Received: 15 December 2022
Accepted: 11 May 2023

Abstract

In this work we provide a novel class of degenerate solutions to the Dirac equation for massive particles, where the rotation of the spin of the particles is synchronized with the rotation of the magnetic field of the wave-like electromagnetic fields corresponding to these solutions. We show that the state of the particles does not depend on the intensity of the electromagnetic fields, but only on their frequency, which is proportional to the mass of the particles and lies in the region of Gamma/X-rays for typical elementary charged particles, such as electrons and protons. We have also calculated the electric current density corresponding to the electromagnetic 4-potentials connected to the degenerate solutions and found that it has the same spatial and temporal dependence on the electromagnetic fields, rotating at an exceptionally high frequency. This result indicates that the degenerate states may occur at locations where matter collapses, e.g., in the central region of a black hole. Finally, we have calculated the spin of the particles described by degenerate spinors and found that it rotates in synchronization with the magnetic field and the current density.