Polarization of the Vacuum of the Quantized Spinor Field by a Topological Defect in the Two-Dimensional Space

The two-dimensional space with a topological defect is a transverse section of the three-dimensional space with an Abrikosov–Nielsen–Olesen vortex, i.e. a gauge-flux-carrying tube which is impenetrable for quantum matter. Charged spinor matter field is quantized in this section with the most general mathematically admissible boundary condition at the edge of the defect. We show that a current and a magnetic field are induced in the vacuum. The dependence of results on the boundary conditions is studied, and we find that the requirement of finiteness of the total induced vacuum magnetic flux removes an ambiguity in the choice of boundary conditions. The differences between the cases of massive and massless spinor matters are discussed.