Sphereplate Casimir interaction in (D + 1)dimensional spacetime
In this paper, we derive the formula for the Casimir interaction energy between a sphere and a plate in (D + 1)dimensional Minkowski spacetime. It is assumed that the scalar field satisfies the Dirichlet or Neumann boundary conditions on the sphere and the plate. As in the D = 3 case, the formula is of TGTG type. One of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general D. Using orthogonality of Gegenbauer polynomials, it turns out that the final TGTG formula for the Casimir interaction energy can be simplified to one that is similar to the D = 3 case. To illustrate the application of the formula, both large separation and small separation asymptotic behaviors of the Casimir interaction energy are computed. The large separation leading term is proportional to L{sup āD+1} if the sphere is imposed with Dirichlet boundary condition, and to L{sup āDā1} if the sphere is imposed with Neumann boundary condition, where L is distance from the center of the sphere to the plane. For the small separation asymptotic behavior, it is shown that the leading term is equal to the one obtainedmore »
 Authors:

^{[1]}
 Department of Applied Mathematics, Faculty of Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan (Malaysia)
 Publication Date:
 OSTI Identifier:
 22250799
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; BOUNDARY CONDITIONS; CORRECTIONS; DIRICHLET PROBLEM; INTERACTIONS; MATRICES; PERTURBATION THEORY; PLATES; POLYNOMIALS; SCALAR FIELDS; SPACETIME; SPHERES; WAVE PROPAGATION