We investigate the vacuum expectation value of the fermionic current induced by a magnetic flux in a (2 þ 1)-dimensional conical spacetime in the presence of a circular boundary. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, a special case of boundary conditions at the cone apex is considered, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. We observe that the vacuum expectation values for both the charge density and azimuthal current are periodic functions of the magnetic flux with the period equal to the flux quantum whereas the expectation value of the radial component vanishes. For both exterior and interior regions, the expectation values of the current are decomposed into boundary-free and boundary-induced parts. For a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. Two integral representations are given for the boundary-free part in the case of a massive fermionic field for arbitrary values of the opening angle of the cone and magnetic flux. The behavior of the induced fermionic current is investigated in various asymptotic regions of the parameters. At distances from the boundary larger than the Compton wavelength of the fermion particle, the vacuum expectation values decay exponentially with the decay rate depending on the opening angle of the cone. We make a comparison with the results already known from the literature for some particular cases.
The vacuum expectation values of the energy-momentum tensor and the fermionic condensate are analyzed for a massive spinor field obeying the MIT bag boundary condition on a cylindrical shell in the cosmic string spacetime. Both regions inside and outside the shell are considered. By applying to the corresponding mode-sums a variant of the generalized Abel-Plana formula, we explicitly extract the parts in the expectation values corresponding to the cosmic string geometry without boundaries. In this way the renormalization procedure is reduced to that for the boundary-free cosmic string spacetime. The parts induced by the cylindrical shell are presented in terms of integrals rapidly convergent for points away from the boundary. The behavior of the vacuum densities is investigated in various asymptotic regions of the parameters. In the limit of large values of the planar angle deficit, the boundary-induced expectation values are exponentially suppressed. As a special case, we discuss the fermionic vacuum densities for the cylindrical shell on the background of the Minkowski spacetime.
We study the nonrelativistic quantum scattering problem of a charged or massive particle by the global monopole background metric. In addition to the purely gravitational effects, we consider the electrostatic or gravitational self-interaction. ͓S0556-2821͑97͒04014-9͔
We study both global as well as local (Nielsen-Olesen) strings in de Sitter
space. While these type of topological defects have been studied in the
background of a de Sitter metric previously, we study here the full set of
coupled equations. We find only ``closed'' solutions. The behaviour of the
metric tensor of these solutions resembles that of ``supermassive'' strings
with a curvature singularity at the cosmological horizon. For global strings
(and the composite defect) we are able to construct solutions which are regular
on the interval from the origin to the cosmological horizon if the global
string core lies completely inside the horizon.Comment: 11 Revtex-pages including 5 ps-figures; v1: typos corrected, note
added; v2: minor changes in conclusion
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