Induced vacuum bosonic current by magnetic flux in a higher dimensional compactified cosmic string spacetime

摘要

In this paper, we analyse the bosonic current densities induced by a magneticflux running along an idealized cosmic string in a high-dimensional spacetime,admitting that the coordinate along the string's axis is compactified.Additionally we admit the presence of an magnetic flux enclosed by thecompactification axis. In order to develop this analysis we calculate thecomplete set of normalized bosonic wave-functions obeying a quasiperiodicitycondition, with arbitrary phase $\beta$, along the compactified dimension. Inthis context, only azimuthal and axial currents densities take place. As to theazimuthal current, two contributions appear. The first contribution correspondsto the standard azimuthal current in a cosmic string spacetime withoutcompactification, while the second contribution is a new one, induced by thecompactification itself. The latter is an even function of the magnetic fluxenclosed by the string axis and is an odd function of the magnetic flux alongits core with period equal to quantum flux, $\Phi_0=2\pi/e$. On the other hand,the nonzero axial current density is an even function of the magnetic fluxalong the core of the string and an odd function of the magnetic flux enclosedby it. We also find that the axial current density vanishes for untwisted andtwisted bosonic fields in the absence of the magnetic flux enclosed by thestring axis. Some asymptotic expressions for the current density are providedfor specific limiting cases of the physical parameter of the model.