Polarization of the vacuum of quantized spinor field by a topological defect in two-dimensional space

TL;DR

This paper investigates how a topological defect in a two-dimensional quantum spinor field induces vacuum polarization effects, including currents and magnetic fields, with results depending on boundary conditions and particle mass.

Contribution

It provides a comprehensive analysis of vacuum polarization by a topological defect in 2D space, clarifying boundary condition effects and the role of particle mass.

Findings

Vacuum induces a current and magnetic field near the defect.

Finiteness of total induced magnetic flux constrains boundary conditions.

Differences between massive and massless spinor cases are discussed.

Abstract

Two-dimensional space with a topological defect is a transverse section of three-dimensional space with the 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 the results on 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 cases of massive and massless spinor matter are discussed.