Vorticity of Twisted Spinor Fields

TL;DR

This paper investigates the vorticity structure of twisted spinor fields, highlighting the non-singular vortex center in a specific current calculation and clarifying conflicting results in the literature.

Contribution

It identifies the unique current formulation that yields a non-singular vortex center and clarifies the apparent contradictions in previous studies.

Findings

Most velocity calculations show singular vorticity at the vortex line.

The Dirac bilinear current without derivatives produces a non-singular vortex center.

The paper resolves conflicts in existing literature regarding vortex singularities.

Abstract

Spinor fields with a vortex structure in free space that allow them to have arbitrary integer orbital angular momentum along the direction of motion have been studied for some time. Relatively new is the observation in a certain context that the vortex center of this field structure is, unlike a classical whirlpool, not singular. We point out that there are several ways to calculate the local velocity of the spinor field and that all but one show a singular vorticity at the vortex line. That one, using the Dirac bilinear current with no derivatives, is the only one so far (to our knowledge) studied in the literature in this context and we further show how to understand an apparent conflict in the existing results.