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We consider matrix structures in the quantum N-body problem that generalize the Faddeev components for resolvents, T-matrices, and eigenfunctions of the continuous spectrum. We write matrix equations for the introduced components of T-matrices and resolvents and use these equations to obtain matrix operators generalizing the matrix three-particle Faddeev operators to the case of arbitrarily many particles. We determine the eigenfunctions of the continuous spectrum of these matrix operators. [ABSTRACT FROM AUTHOR]

Two different types of orthogonality condition models (OCM) are equivalently formulated in the Faddeev formalism. One is the OCM which uses pairwise orthogonality conditions for the relative motion of clusters, and the other is the one which uses the orthogonalizing pseudo-potential method. By constructing a redundancy-free T-matrix, one can exactly eliminate the redundant components of the total wave function for the harmonic-oscillator Pauli-forbidden states, without introducing any limiting procedure. As an example, a three-α-particle model interacting via the deep αα potential by Buck, Friedrich, and Wheatley is investigated. [ABSTRACT FROM AUTHOR]