Core structure and oscillations of spinor vortices

Abstract

We describe the topological vortices of spinor fields. The topological group of the invariant manifold is (U(1)⊛SU(2)) Z 2 , and the circulation of the vortex is half the one of a complex scalar field. In the context of a Galilean invariant theory, the vortex core structure is non-analytical at its axis. Since the typical speed becomes very large in the inner vortex core, one must include relativistic effects. We discuss the stability of non-relativistic vortices under the first relativistic correction. Furthermore, spinorial fields satisfying the Dirac equation possess vortices with an analytic behavior in the core that becomes locally magnetized. The relativistic inner core structure matches the non-relativistic solution at a distance of the order of the Compton length.