Fermionic vacuum polarization by a magnetic tube in the cosmic string spacetime

TL;DR

This paper investigates the effects of a magnetic tube on fermionic vacuum polarization in cosmic string spacetime, analyzing different magnetic field configurations and their impact on fermionic condensates and energy-momentum tensor expectations.

Contribution

It provides explicit solutions for fermionic wave-functions in three magnetic field configurations and decomposes vacuum expectation values into flux-dependent and core-induced parts.

Findings

Vacuum expectation values are decomposed into zero-thickness and core-induced contributions.

Core-induced effects depend on total magnetic flux and are generally not periodic.

The energy-momentum tensor is diagonal, conserved, and its trace relates to the fermionic condensate.

Abstract

In this paper, we consider a charged massive fermionic quantum field in the idealized cosmic string spacetime and in the presence of a magnetic field confined in a cylindrical tube of finite radius. Three distinct configurations for the magnetic fields are taken into account: (i) a cylindrical shell of radius $a$, (ii) a magnetic field proportional to $1/r$ and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius $a$ coincides with the cosmic string. Our main objectives in this paper are to analyze the fermionic condensat (FC) e and the vacuum expectation value (VEV) of the fermionic energy-momentum tensor. In order to do that, we explicitly construct the complete set of normalized wave-functions for each configuration of magnetic field. We show that in the region outside the tube, the FC and the VEV of the energy-momentum tensor are decomposed into two parts: the first ones correspond to the zero-thickness magnetic flux contributions, and the seconds are induced by the non-trivial structure of the magnetic field, named core-induced contributions. The latter present specific forms depending on the magnetic field configuration considered. We also show that the VEV of the energy-momentum tensor is diagonal, obeys the conservation condition and its trace is expressed in terms of the fermionic condensate. The zero-thickness contributions to the FC and VEV of the energy-momentum tensor, depend only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contributions they depend on the total magnetic flux inside the tube, and consequently, in general, are not a periodic function of the magnetic flux.