The N-representability problem, the pseudo-spectral decomposition of antisymmetric 1-body operators, and collective behaviour

The pseudo-spectral decomposition of an N-particle antisymmetric 1-body positive-semidefinite operator that corresponds to the canonical convex decomposition into the extreme elements of the dual cone of the set of fermion N-representable 1-density operators has been derived. An attempt at constructing a mathematical model for collective behaviour of a system of N fermions that originates from the pseudo-spectral decomposition is presented.