Relativistic quantum-mechanical description of twisted paraxial electron and photon beams

Abstract

The analysis of twisted (vortex) paraxial photons and electrons is fulfilled in the framework of relativistic quantum mechanics. The use of the Foldy-Wouthuysen representation radically simplifies the description of relativistic electrons and clarifies the fundamental properties of twisted particles. It is demonstrated that the twisted and other structured photons are luminal. Their subluminality apparently takes place because the photon energy is also contributed by a hidden motion. This motion is vanished by averaging and disappears in the semiclassical description based on expectation values of the momentum and velocity operators. It is proven that semiclassical quanta of structured light are subluminal and massive. The quantum-mechanical and semiclassical descriptions of twisted and other structured electrons lead to similar results. The effect of a quantization of the velocity and the effective mass of the structured photon and electron is predicted. This effect is observable for the photon. The twisted and untwisted semiclassical photons and electrons modeled by the centroids are considered in the accelerated and rotating noninertial frame. The coincidence of their inertial masses with kinematic ones is shown. The orbital magnetic moment of the Laguerre-Gauss electron does not depend on the radial quantum number.