Cluster-Decomposition Properties ofϕ3-Perturbation-Theory Amplitudes at High Energy

We establish that a cluster-decomposition technique, similar to that used in statistical mechanics, can be applied to the study of high-energy scattering processes. In particular, we examine in detail the multiperipheral amplitudes in a ${\varphi }^3$ field theory with one space and one time dimension. The cluster decomposition provides (1) a mathematically elegant and physically intuitive way of treating terms nonleading in ${\left(\ln s\right)}^n$, (2) a framework in which the Regge asymptotic behavior of the scattering amplitude emerges naturally; and (3) a direct means of calculating the one-particle and multiparticle spectra in inclusive reactions. In addition, we consider further possible applications of the technique, including its extension to a ${\varphi }^3$ theory with three space and one time dimension. Here we establish a simple criterion, based on the form of the cluster decomposition, to determine whether a set of amplitudes leads to a Regge pole or to a more complicated singularity structure.