  We calculate the effective fluctuation induced force between spherical or
disk-like colloids trapped at a flat, fluid interface mediated by thermally
excited capillary waves. This Casimir type force is determined by the partition
function of the system which in turn is calculated in a functional integral
approach, where the restrictions on the capillary waves imposed by the colloids
are incorporated by auxiliary fields. In the long-range regime the fluctuation
induced force is shown to depend sensitively on the boundary conditions imposed
at the three-phase contact line between the colloids and the two fluid phases.
The splitting of the fluctuating capillary wave field into a mean-field and a
fluctuation part leads to competing repulsive and attractive contributions,
respectively, which give rise to cancellations of the leading terms. In a
second approach based on multipole expansion of the Casimir interaction, these
cancellations can be understood from the vanishing of certain multipole moments
enforced by the boundary conditions. We also discuss the connection of the
different types of boundary conditions to certain external fields acting on the
colloids which appear to be realizable by experimental techniques such as the
laser tweezer method.
