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

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 $δ$-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.