Magnetic field in vacuum of quantum spinor matter induced by a cosmic string in three-dimensional space

TL;DR

This paper investigates the quantum vacuum effects of a cosmic string modeled as a magnetic flux tube in three-dimensional space, focusing on the induced magnetic flux and boundary conditions for spinor matter.

Contribution

It provides a comprehensive analysis of the vacuum magnetic flux induced by a cosmic string in (3+1)D, identifying the unique boundary condition that ensures finite flux.

Findings

Induced vacuum magnetic flux depends on the tube's size and flux.

Only the MIT bag boundary condition yields finite total flux.

The effect varies with the tube's transverse size and internal flux.

Abstract

A linear magnetic topological defect (cosmic string) is modeled as a magnetic flux-carrying tube that is impenetrable to external spinor matter. The matter field is quantized in the background of this tube, with the most general set of boundary conditions ensuring both the tube's impenetrability and the self-adjointness of the Dirac Hamiltonian operator. We compute the induced vacuum magnetic flux along the tube in (3+1)-dimensional space-time. It was shown that the requirement for the total induced vacuum magnetic flux to be finite restricts the admissible boundary conditions to only one choice: the MIT quark bag boundary condition. The dependence of the effect on the transverse size of the tube and the flux inside the tube was also analyzed.