  In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian
model for systems with short-ranged intermolecular forces. Starting from a
microscopic Landau-Ginzburg-Wilson Hamiltonian with a double parabola
potential, we reformulate the derivation of the interfacial model using a
rigorous boundary integral approach. This is done for three scenarios: a single
fluid phase in contact with a nonplanar substrate (i.e., wall); a free
interface separating coexisting fluid phases (say, liquid and gas); and finally
a liquid-gas interface in contact with a nonplanar confining wall, as is
applicable to wetting phenomena. For the first two cases our approaches
identifies the correct form of the curvature corrections to the free energy
and, for the case of a free interface, it allows us to recast these as an
interfacial self-interaction as conjectured previously in the literature. When
the interface is in contact with a substrate our approach similarly identifies
curvature corrections to the nonlocal binding potential, describing the
interaction of the interface and wall, for which we propose a generalized and
improved diagrammatic formulation.
