  In this paper we try to work out in detail the implications of a microscopic
theory for capillary waves under the assumption that the density is given along
lines normal to the interface. Our study provides interface Hamiltonians for
adsorbed films in a variety of systems, and shows that the corrections to the
classical capillary wave spectrum are of the same order as the surface tension.
This implies that it is possible, at least in principle, to measure them in
x-ray surface scattering experiments. Interestingly, our study also sheds some
light on the nature of the liquid-vapor interface in the absence of external
fields and allows us to reconcile the Fisk-Widom scaling hypothesis with
capillary wave theory.
