SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC D-DIMENSIONAL SPHERES

Abstract

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel–Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between (D-1)-dimensional surfaces, close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force.