The Casimir Problem of Spherical Dielectrics: A Solution in Terms of Quantum Statistical Mechanics

摘要

The Casimir energy for a compact dielectric sphere is considered in a novelway, using the quantum statistical method introduced by H\oye - Stell andothers. Dilute media are assumed. It turns out that this method is a verypowerful one: we are actually able to derive an expression for the Casimirenergy that contains also the negative part resulting from the attractive vander Waals forces between the molecules. It is precisely this part of theCasimir energy that has turned out to be so difficult to extract from theformalism when using the conventional field theoretical methods for acontinuous medium. Assuming a frequency cutoff, our results are in agreementwith those recently obtained by Barton [J. Phys. A: Math. Gen. 32(1999)525].