The particle-hole component of the 2-particle green function—its relation to the canonical particle-hole states and its N-representability

The relation between the 2-particle Green function and the projections of the excited states onto the particle-hole space of the ground state of a fermion system is derived for the case in which the spectrum of the Green function is totally discrete. From this relation, the conditions for the N-representability of the 2-particle Green function are obtained, as is an explicit representation of the projection operator for the particle-hole space. The projection operator for the 2-particle-2-hole space is also presented.