Vacuum Polarization in the Presence of Magnetic Flux at Finite Temperature in the Cosmic String Background

TL;DR

This paper investigates how finite temperature and magnetic flux influence vacuum polarization effects of a charged massless scalar field around a cosmic string, considering different magnetic field configurations and calculating the associated Green functions.

Contribution

It provides a detailed analysis of vacuum polarization at finite temperature in a cosmic string background with magnetic flux, including explicit calculations of Green functions for different magnetic field profiles.

Findings

Finite temperature affects the vacuum expectation value of the scalar field squared.

Magnetic flux configurations influence the vacuum polarization effects.

The study offers explicit Green function calculations for the considered setup.

Abstract

In this paper we analyse the vacuum polarization effect associated with the charged massless scalar field, in the presence of magnetic flux at finite temperature, in the cosmic string background. We consider a spacetime of an idealized cosmic string which presents a magnetic field confined in a cylindrical tube of finite radius. Two different situations are taken into account in our analysis: (i) a homogeneous field inside the tube and (ii) a magnetic field proportional to $1/r$. In these two cases, the axis of the infinitely long tube of radius $R$ coincides with the cosmic string. Specifically, we calculate the effects produced by the temperature in the renormalized vacuum expectation value of the square of the charged massless scalar field, $<\hat{\phi}^{\ast}(x)\hat{\phi}(x)>$. Therefore, in order to realize these analysis, we calculate the Euclidean Green function associated with this field in this background.