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arXiv · 1511.02745

Induced fermionic current by a magnetic tube in the cosmic spacetime

M. S. Maior de Sousa·R. F. Ribeiro·E. R. Bezerra de Mello
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Abstract

In this paper, we consider a charged massive fermionic quantum field in the space-time of an idealized cosmic string, in the presence of a magnetic field confined in a cylindrical tube of finite radius. Three distinct configurations for the magnetic field is 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 objective is to analyze the induced vacuum fermionic current densities outside the tube. In order to do that, we explicitly construct the wave-functions inside and outside the tube for each case. Having the complete set of normalized wave-functions, we use the summation method to develop our analysis. We show that in the region outside the tube, the induced currents are decomposed into a parts corresponding to a zero-thickness magnetic flux in addition to a core-induced contributions. The latter presents specific form depending on the magnetic field configuration considered. We also see that the only non-vanishing component of fermionic current corresponds to the azimuthal one. The zero-thickness contribution depends only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contribution, it depends on the total magnetic flux inside the tube, and consequently, in general, it is not a periodic function of the flux.

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M. S. Maior de Sousa, R. F. Ribeiro, E. R. Bezerra de Mello. 2015-11-09. Induced fermionic current by a magnetic tube in the cosmic spacetime. https://doi.org/10.1103/physrevd.93.043545

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