Js. Hoye et I. Brevik, The Casimir problem of spherical dielectrics: A solution in terms of quantum statistical mechanics, J STAT PHYS, 100(1-2), 2000, pp. 223-232
The Casimir energy for a compact dielectric sphere is considered in a novel
way, using the quantum statistical method introduced by Hoye and 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 v
an 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-theoretic methods for a continu
ous medium. Assuming a frequency cutoff, our results are in agreement with
those recently obtained by G. Barton.