Twisted Localized Solutions of the Dirac Equation: Hopfion-like States of Relativistic Electrons

Abstract

All known solutions of the Dirac equation describing states of electrons endowed with angular momentum are very far from our notion of the electron as a spinning charged bullet because they are not localized in the direction of propagation. We present here analytic exact solutions, eigenstates of the total angular momentum component $M_z$, that come very close to this notion. These new solutions of the Dirac equation have also intricate topological properties similar to the hopfion solutions of the Maxwell equations.

Submitted to Phys. Rev. A

References in corpus (3)

• Electromagnetic Angular Momentum
• Electromagnetic Force and Momentum
• Relativistic electron wave packets carrying angular momentum

Cited by in corpus (8)

• Semiclassical probability of radiation of twisted photons in the ultrarelativistic limit
• Backflow in relativistic wave equations
• Construction of Dirac spinors for electron vortex beams in background electromagnetic fields
• New solutions of the Dirac, Maxwell and Weyl equations from the fractional Fourier transform
• Vortex Structures and Momentum Sharing in Dynamic Sauter-Schwinger Process
• Scattering of a twisted electron wavepacket by a finite laser pulse
• Localized degenerate solutions to the massless Dirac and Weyl equations
• Comment on "Fractional Angular Momenta, Gouy and Berry Phases in Relativistic Bateman-Hillion-Gaussian Beams of Electrons" [arXiv:1812.04957]