  A formulation is developed for the calculation of the
electromagnetic--fluctuation forces for dielectric objects of arbitrary
geometry at small separations, as a perturbative expansion in the dielectric
contrast. The resulting Lifshitz energy automatically takes on the form of a
series expansion of the different many-body contributions. The formulation has
the advantage that the divergent contributions can be readily determined and
subtracted off, and thus makes a convenient scheme for realistic numerical
calculations, which could be useful in designing nano-scale mechanical devices.
