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

Abstract

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.

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. A

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• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
• Summation formula over the zeros of the associated Legendre function with a physical application
• Local zeta regularization and the scalar Casimir effect II. Some explicitly solvable cases