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

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