Self-energy and Self-force in the Space-time of a Thick Cosmic String

We calculate the self-energy and self-force for an electrically charged particle at rest in the background of Gott-Hiscock cosmic string space-time. We found the general expression for the self-energy which is expressed in terms of the $S$ matrix of the scattering problem. The self-energy continuously falls down outward from the string's center with maximum at the origin of the string. The self-force is repulsive for an arbitrary position of the particle. It tends to zero in the string's center and also far from the string and it has a maximum value at the string's surface. The plots of the numerical calculations of the self-energy and self-force are shown.Comment: 15 pages, 4 Postscript figures, ReVTe

Classical self-forces in a space with a dispiration

We derive the gravitational and electrostatic self-energies of a particle at rest in the background of a cosmic dispiration (topological defect), finding that the particle may experience potential steps, well potentials or potential barriers depending on the nature of the interaction and also on certain properties of the defect. The results may turn out to be useful in cosmology and condensed matter physics.Comment: 5 pages, 4 figures, revtex4 fil

Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension

In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a contour integral representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a $d$-dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly.Comment: 26 Pages, 1 Figur

Relative-zeta and Casimir energy for a semitransparent hyperplane selecting transverse modes

We study the relative zeta function for the couple of operators $A_0$ and $A_\alpha$, where $A_0$ is the free unconstrained Laplacian in $L^2(\mathbf{R}^d)$ ($d \geq 2$) and $A_\alpha$ is the singular perturbation of $A_0$ associated to the presence of a delta interaction supported by a hyperplane. In our setting the operatorial parameter $\alpha$, which is related to the strength of the perturbation, is of the kind $\alpha=\alpha(-\Delta_{\parallel})$, where $-\Delta_{\parallel}$ is the free Laplacian in $L^2(\mathbf{R}^{d-1})$. Thus $\alpha$ may depend on the components of the wave vector parallel to hyperplane; in this sense $A_\alpha$ describes a semitransparent hyperplane selecting transverse modes. As an application we give an expression for the associated thermal Casimir energy. Whenever $\alpha=\chi_{I}(-\Delta_{\parallel})$, where $\chi_{I}$ is the characteristic function of an interval $I$, the thermal Casimir energy can be explicitly computed.Comment: 21 page

Fermionic current induced by magnetic flux in compactified cosmic string spacetime

In this paper, we investigate the fermionic current densities induced by a magnetic flux running along the idealized cosmic string in a four-dimensional spacetime, admitting that the coordinate along the string's axis is compactified. In order to develop this investigation we construct the complete set of fermionic mode functions obeying a general quasiperiodicity condition along the compactified dimension. The vacuum expectation value of the azimuthal current density is decomposed into two parts. The first one corresponds to the uncompactified cosmic string geometry and the second one is the correction induced by the compactification. For the first part we provide a closed expression which includes various special cases previously discussed in the literature. The second part is an odd periodic function of the magnetic flux along the string axis with the period equal to the flux quantum and it is an even function of the magnetic flux enclosed by the string axis. The compactification of the cosmic string axis in combination with the quasiperiodicity condition leads to the nonzero axial current density. The latter is an even periodic function of the magnetic flux along the string axis and an odd periodic function of the magnetic flux enclosed by the string axis. The axial current density vanishes for untwisted and twisted fields in the absence of the magnetic flux enclosed by the string axis. The asymptotic behavior of the vacuum fermionic current is investigated near the string and at large distances from it. In particular, the topological part of the azimuthal current and the axial current are finite on the string's axis.Comment: 22 pages, 4 figure