Transition amplitudes in the N -body Faddeev-type theory

Within the framework of the Faddeev-type $N$ -body scattering formalism, we find the transition operators for all $N$ -body processes that start from two-cluster initial states, and construct the $N$ -body Faddeev-type equations they satisfy. In particular, we show that our previous $N$ -body generalizations of the three-body operator ${K}_{\ensuremath{\beta}\ensuremath{\alpha}}$ correspond to the $N$ -body scattering amplitudes for complete breakup, and that the Alt-Grassberger-Sandhas $N$ -body generalizations of the three-body transition operator ${U}_{\ensuremath{\beta}\ensuremath{\alpha}}$ correspond to $N$ -body elastic and rearrangement amplitudes. As an introduction, we give a simple derivation of the $N$ -body Faddeev-type equations for the wave-function components.