Vacuum Polarization of a Charged Massless Fermionic Field by a Magnetic Flux in the Cosmic String Spacetime

TL;DR

This paper computes the vacuum energy-momentum tensor for massless fermionic fields influenced by magnetic fluxes in cosmic string spacetime, considering different magnetic field configurations and accounting for finite tube thickness effects.

Contribution

It introduces explicit calculations of Euclidean Feynman propagators for various magnetic flux configurations, including finite thickness effects, in cosmic string spacetime.

Findings

Finite thickness of magnetic tubes significantly affects vacuum averages.

Derived new parts of propagators due to finite tube radius.

Quantified contributions of magnetic flux configurations to energy-momentum tensor.

Abstract

We calculate the vacuum averages of the energy-momentum tensor associated with a massless left-handed spinor fields due to magnetic fluxes on idealized cosmic string spacetime. In this analysis three distinct configurations of magnetic fields are considered: {\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 tubes of radius $R$ coincides with the cosmic string. In order to proceed with these calculations we explicitly obtain the Euclidean Feynman propagators associated with these physical systems. As we shall see, these propagators possess two distinct parts. The first are the standard ones, i.e., corresponding to the spinor Green functions associated with the massless fermionic fields on the idealized cosmic string spacetime with a magnetic flux running through the line singularity. The second parts are new, they are due to the finite thickness of the radius of the tubes. As we shall see these extra parts provide relevant contributions to the vacuum averages of the energy-momentum tensor.