Geometrically invariant interactions in capillary wave surface models

The authors examine the role of geometrically invariant interactions, such as curvature, in modulating the long-distance behaviour of surface tension models in the context of a perturbative epsilon -expansion approach first discussed by Wallace and Zia (1979). A suggestive semiclassical calculation shows how some of these interactions arise. The renormalisation and, hence, scaling properties of the simplest of these interactions, the contraction of the second fundamental form with the metric tensor (g.b) are considered.