Fermionic vacuum polarization by a magnetic tube in the cosmic string spacetime
arXiv:1610.05599 · doi:10.1103/PhysRevD.95.045005
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 , (ii) a magnetic field proportional to and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius 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.
arXiv comment23 pages, 4 figures. Version accepted for publication in PRD. arXiv admin note: text overlap with arXiv:1511.02745
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