Vacuum Polarization of a Charged Massless Scalar Field on Cosmic String Spacetime in the Presence of a Magnetic Field

TL;DR

This paper investigates vacuum polarization effects of a charged massless scalar field around a cosmic string with a confined magnetic field, analyzing three magnetic configurations via Green function calculations.

Contribution

It provides explicit calculations of the Euclidean Green function for different magnetic field configurations around a cosmic string.

Findings

Vacuum polarization effects depend on magnetic field configuration.

Explicit Green functions are derived for three magnetic field models.

Results enhance understanding of quantum fields in cosmic string spacetimes.

Abstract

In this paper we consider a charged massless scalar quantum field operator in the spacetime of an idealized cosmic string, i.e., an infinitely long, straight and static cosmic string, which presents a magnetic field confined in a cylindrical tube of finite radius. Three distinct situations are taking into account in this analysis: {\it{i)}} a homogeneous field inside the tube, {\it{ii)}} a magnetic field proportional to $1/r$ and {\it{iii)}} a cylindrical shell with $\delta$-function. In these three cases the axis of the infinitely long tube of radius $R$ coincides with the cosmic string. In order to study the vacuum polarization effects outside the tube, we explicitly calculate the Euclidean Green function associated with this system for the three above situations, considering points in the region outside the tube.