Azimuthal Fermionic Current in the Cosmic String Spacetime Induced by a Magnetic Tube

Abstract In this paper, we calculate the vacuum expectation value of the azimuthal fermionic current, associated with a massive fermionic quantum field in the spacetime of an idealized cosmic string, considering the presence of a magnetic tube of radius a, coaxial to the string. In this analysis three distinct configurations of magnetic field are considered: (i) a magnetic field concentrated on a surface of the tube; (ii) a magnetic field presenting a 1 / r radial dependence; and (iii) an homogeneous magnetic field. In order to develop this analysis , we construct the complete set of normalized solution of the Dirac equation in the region outside the tube. By using the mode-sum formula, we show that the azimuthal induced current is formed by two contributions: the first being the current induced by a line of magnetic flux running along the string, and the second, named core-induced current, is induced by the non-vanishing extension of the magnetic tube. The first contribution depends only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one; as to the second contribution, it depends on the total magnetic flux. We specifically analyze the core-induced current in several limits of the parameters and distance to the tube. View Full-Tex