Abstract
In this paper we consider a charged massless scalar quantum field operator in the spacetime of an idealized cosmic string which presents a magnetic field confined in a cylindrical tube of finite radius. Three distinct situations are taken into account in this analysis. In three cases the axis of the infinitely long tube of radius R coincides with the cosmic string. Because we study the combined gravitational and electromagnetic Aharanov-Bohm effect, we calculate the vacuum polarization effects outside the tube.
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