A systematic treatment of cluster models in multiparticle dynamics

Generalizing the leading ideas and the standard methods of modern approaches to the N-body problem, we devise direct procedures for describing the dynamics of clustered N-body systems. We show that these procedures, leading to m-cluster integral equations, can be developed starting from any type of multiparticle coupling scheme. Cluster models are formulated in the framework of the Faddeev-Yakubovskii coupling scheme (both in the original sophisticated language and, more simply, in terms of variables with artificial indexes) as well as in the context of any approach with highly-connected-kernel equations. Our general formulation reproduces all the existing N-particle equations in the limit case m =N.