QFT Limit of the Casimir Force

Abstract

High precision measurements of the Casimir effect and recent applications to micro electromechanical systems raise the question of how large the Casimir force can be made in an arbitrarily small device. Using a simple model for the metal boundary in which the metal is perfectly conducting at frequencies below plasma frequency omega_p and perfectly transparent above such frequency, I find that the Casimir force for plate separations a<lambda_p/2, where lambda_p is the plasma wavelength is given by -(h omega_p^4)/(24 pi^2 c^3) which is independent of a. This result is considered the maximum value of the Casimir force for non-ideal metallic boundaries as calculated by quantum field theory. It differs from predictions of non retarded Van der Waals theory. Implications of this result for geometries different from the planar one and in particular for the hollow metallic sphere are discussed.