Macroscopic theory of Van der Waals force between dielectrics

Abstract

It is shown that Lifshitz' theory of van der Waals interactions between dielectrics can be extended to arbitrary geometry. The van der Waals force density is expressed in terms of the electric Green function of Maxwell's equations. This force density can be shown to be identical to that derived by Dzyaloshinskii and Pitaevskii (1959) from quantum field theoretical considerations. For dissipationless dielectrics the force density agrees with that derived from the free energy as calculated by Casimir's method (1948) of summing over normal modes.