Field-theoretic approach to Reaction-Diffusion Models

A mean-field theory is developed for the Gray-Scott and related reaction-diffusion models. A multiple Hubbard-Stratonovich transformation defines the order parameter and the random-phase- approximation (RPA) fluctuations. The dynamics of the fluctuations of the order parameter are shown to have all the features of the original reaction-diffusion models. We discuss the implications of this approach to the study of pattern formations.