The Proximity Force Approximation for the Casimir Energy of Plate-Sphere and Sphere-Sphere Systems in the Presence of One Extra Compactified Universal Dimension
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The Casimir energies for plate-sphere system and sphere-sphere systems under PFA in the presence of one extra compactified universal dimension are analyzed. We find that the Casimir energy between a plate and a sphere in the case of sphere-based PFA is divergent. The Casimir energy of plate-sphere system in the case of plate-based PFA is finite and keeps negative. The extra-dimension corrections to the Casimir energy will be more manifest if the sphere is larger or farther away from the plate. It is shown that the negative Casimir energy for two spheres is also associated with the sizes of spheres and extra space. The larger spheres and the longer distance between them make the influence from the additional dimension stronger.
KeywordsCasimir energy Kaluza-Klein model
The author thanks Professor K. Milton and Professor M. Bordag for helpful discussions. This work is supported by NSFC No. 10875043 and is partly supported by the Shanghai Research Foundation No. 07dz22020.