Euler fluid mechanics solutions to Dirac quantum mechanics equation using multipolar oscillations in spherical geometry

Abstract

The multipolar spherical vortex solutions to the Euler equations for Newtonian fluids in background cylindrical flow with swirl satisfy, once their three-dimensional Cartesian velocity components are mapped into the components of a four-component complex vector wave function, the relativistic Dirac equation for a free particle. It is suggested that the vertical component of the intrinsic spin angular momentum of the quantum mechanics particles is the azimuthal wavenumber of the angular phase of the oscillation modes in presence of the background rotation.