11 research outputs found

    Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime

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    In this paper we investigate the Wightman function, the renormalized vacuum expectation values of the field square, and the energy-momentum tensor for a massive scalar field with general curvature coupling inside and outside of a cylindrical shell in the generalized spacetime of straight cosmic string. For the general case of Robin boundary condition, by using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases. The generalization of the results to the exterior region is given for a general cylindrically symmetric static model of the string core with finite support.Comment: 21 pages, 5 figure

    Scalar Casimir densities for cylindrically symmetric Robin boundaries

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    Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter in the region between two coaxial cylindrical boundaries. It is assumed that the field obeys general Robin boundary conditions on bounding surfaces. The application of a variant of the generalized Abel-Plana formula allows to extract from the expectation values the contribution from single shells and to present the interference part in terms of exponentially convergent integrals. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. The first one contains well-known surface divergences and needs a further renormalization. The interaction forces between the cylindrical boundaries are finite and are attractive for special cases of Dirichlet and Neumann scalars. For the general Robin case the interaction forces can be both attractive or repulsive depending on the coefficients in the boundary conditions. The total Casimir energy is evaluated by using the zeta function regularization technique. It is shown that it contains a part which is located on bounding surfaces. The formula for the interference part of the surface energy is derived and the energy balance is discussed.Comment: 22 pages, 5 figure

    Exact zero-point interaction energy between cylinders

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    We calculate the exact Casimir interaction energy between two perfectly conducting, very long, eccentric cylindrical shells using a mode summation technique. Several limiting cases of the exact formula for the Casimir energy corresponding to this configuration are studied both analytically and numerically. These include concentric cylinders, cylinder-plane, and eccentric cylinders, for small and large separations between the surfaces. For small separations we recover the proximity approximation, while for large separations we find a weak logarithmic decay of the Casimir interaction energy, typical of cylindrical geometries.Comment: 20 pages, 7 figure

    Whightman function and scalar Casimir densities for a wedge with a cylindrical boundary

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    Whightman function, vacuum expectation values of the field square, and the energy-momentum tensor are investigated for a scalar field inside a wedge with and without a coaxial cylindrical boundary. Dirichlet boundary conditions are assumed on the bounding surfaces. The vacuum energy-momentum tensor is evaluated in the general case of the curvature coupling parameter. Making use of a variant of the generalized Abel-Plana formula, expectation values are presented as the sum of two terms. The first one corresponds to the geometry without a cylindrical boundary and the second one is induced by the presence of this boundary. The asymptotic behaviour of the field square, vacuum energy density and stresses near the boundaries are investigated. The additional vacuum forces acting on the wedge sides due the presence of the cylindrical boundary are evaluated and it is shown that these forces are attractive. As a limiting case, the geometry of two parallel plates perpendicularly intersected by a third one is analyzed.Comment: 19 pages, 6 figures, new section is added on the VEVs for the region outside the cylidrical shell, discussion and references added, accepted for publication in J. Phys.
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