Vacuum polarization around a straight wire carrying a steady current

TL;DR

This paper derives explicit formulas for the vacuum polarization effects, including vector potential, current density, and magnetic field, around a straight wire with steady current, inspired by cosmic string models.

Contribution

It provides the first explicit expressions for vacuum polarization effects around a current-carrying wire, extending theoretical understanding in quantum field theory in curved spacetime.

Findings

Explicit formulas for vector potential, current density, and magnetic field

First-order vacuum polarization effects around a wire

Insights relevant to cosmic string physics

Abstract

Motivated by the example of the superconducting cosmic string which can be a physical representation of a straight wire carrying a steady current, we derive in this case the explicit expressions of the induced vector potential, current density and magnetic field due to the vacuum polarization at the first order in the fine structure constant.