STOCHASTIC GROWTH EQUATIONS AND REPARAMETRIZATION INVARIANCE

This article reviews the role of reparametrization invariance (the inv ariance of the properties of a system with respect to the choice of th e co-ordinate system used to describe it) in deriving stochastic equat ions that describe the growth of surfaces. By imposing reparametrizati on invariance on a system, the authors identify the physical origin of many of the terms in its growth equations. Both continuum-growth equa tions for interfaces and equations for the coarse-grained evolution of discrete-lattice models are derived with this method. A detailed anal ysis of the discrete-lattice case and its small-gradient expansion pro vides a physical basis for terms found in commonly studied growth equa tions. The reparametrization-invariant formulation of growth processes also has the advantage of allowing one to model shadowing effects tha t are lost in the no-overhang approximation and to conserve underlying symmetries of the system that are lost in a small-gradient expansion. Finally, a knowledge of the full equation of motion, beyond the lowes t-order gradient expansion, may be relevant in problems where the usua l perturbative renormalization methods fail.