Nonlinearities in Conservative Growth Equations

Using the dynamic renormalization group (DRG) technique, we analyze general nonlinearities in a conservative nonlinear growth equation with non-conserved gaussian white noise. We show that they fall in two classes only: the Edwards-Wilkinson and Lai-Das Sarma types, by explicitly computing the associated amputated two and three point functions at the first order in perturbation parameter(s). We further generalize this analysis to higher order nonlinearities and also suggest a physically meaningful geometric interpretation of the same.