Space-inversion operator, permutational

We will now derive a Dyson equation by expressing the inverse matrix of the extended two-particle Green s function Qr,y, u ) by a matrix representation of the extended operator H. We already mentioned that the primary set of states l rs) spans a subspace (the model spaice) of the Hilbert space Y. Since the states IVrs) are /r-orthonormal they are also linearly independent and thus form a basis of this subspace. Here and in the following the set of pairs of singleparticle indices (r, s) has to be restricted to r > s for the pp and hh cases (b) and (c) where the states are antisymmetric under permutation of r and s. No restriction applies in the ph case (a). The primary set of states Yr ) can now be extended to a complete basis Qj D Yr ) of the Hilbert space Y. We may further demand that the states Qj) are /r-orthonormal ... 

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