Polarization of the vacuum of a quantized scalar field by an impenetrable magnetic vortex of finite thickness

TL;DR

This paper investigates how a finite-sized magnetic vortex influences the vacuum polarization of a quantized scalar field, revealing finite, flux-dependent vacuum energy effects relevant to cosmic string physics.

Contribution

It demonstrates that a finite magnetic flux tube induces a finite, periodic vacuum energy in a scalar field, especially when the Compton wavelength exceeds the tube's size.

Findings

Vacuum energy is finite and periodic in magnetic flux.

Vacuum polarization effects are significant when the Compton wavelength is large.

Results have implications for cosmic-string background studies.

Abstract

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the tube. It is shown that, if the Compton wavelength associated with the scalar field exceeds considerably the transverse size of the tube, then the vacuum energy which is finite and periodic in the value of the magnetic flux enclosed in the tube is induced on a plane transverse to the tube. Some consequences for generic features of the vacuum polarization in the cosmic-string background are discussed.