On the equivalence of Reggeon field theory in zero transverse dimensions and reaction-diffusion processes

The Reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows at most triple pomeron interactions and the other that embodies an additional 2-->2 quartic Reggeon coupling. The behavior of the scattering amplitude at asymptotic rapidities is obtained in both cases. In an s-channel picture of the high energy scattering both models can be viewed as reaction-diffusion processes. We derive known results in Reggeon field theory rather easily using the reaction-diffusion formalism. We find that some results which are surprising from the Reggeon field theory point of view turn out to have a simple interpretation from the reaction-diffusion point of view.