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

Abstract

In this paper, we analyse the bosonic current densities induced by a magnetic flux 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 the compactification axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave-functions obeying a quasiperiodicity condition, with arbitrary phase β, along the compactified dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first contribution corresponds to the standard azimuthal current in a cosmic string spacetime without compactification, while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the string axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, Φ 0 = 2π/e. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by it. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the string axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.

Induced vacuum bosonic current in a compactified cosmic string spacetime

“…The above axial current density, in the massless limit, matches to the result for the Minkowski spacetime times the conformal factor (τ /α) 4 (the sign of the axial current obtained in [34] should be corrected to the opposite one).…”

“…The summation above has been developed in [34]. The result is The integral over z can be evaluated with the help of the formula [43] ∞…”

“…In these papers, the authors have shown that induced vacuum current densities along the azimuthal direction arise if the ratio of the magnetic flux by the quantum one has a nonzero fractional part. The calculation of induced bosonic and fermionic currents in higher-dimensional cosmic string spacetime in the presence of a magnetic flux has been developed in [34,35]. The induced fermionic current by a magnetic flux in (2 + 1)-dimensional conical spacetime and in the presence of a circular boundary has also been analyzed in [36].…”

Vacuum expectation value of the energy-momentum tensor in a higher-dimensional compactified cosmic string spacetime

“…The main reason is in the expression for the function g(q, α 0 , 2y), Eq. (40), that appears in the integral. Being α 0 = 0, there are no hyperbolic cosines involving the variable of integration, y, and the integral is finite.…”

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

“…In all these analysis, the authors have shown that induced azimuthal vacuum current densities take place if the ratio of the magnetic flux by the quantum one has a nonzero fractional part. In fact, induced fermionic and scalar current densities in compactified cosmic string spacetimes have been considered in [15,16].…”