2016/10/31 by M. S. Maior de Sousa, R. Freire Ribeiro, E. R. Bezerra de Mello
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1103/physrevd.95.045005
published as Phys. Rev. D 95, 045005 (2017) · 23 pages, 4 figures. Version accepted for publication in PRD. arXiv admin note: text overlap with arXiv:1511.02745
arxiv created 2017/01/24 · arxiv updated 2017/02/22
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.