Flutuações quânticas fermiônicas induzidas por um tubo magnético no espaço-tempo de uma corda cósmica

Abstract

In this work, 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 vacuum expected values (VEVs) of the current density, jP, fermionic condensate (FC) e and the VEV of the fermionic energy-momentum tensor, Ti". 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 current density, 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.