As has been shown by TOMASINI it is possible to develop a perturbation theory for a many-fermion system by starting with a BOGOLJUBOV-transformed HAMILTONian having an energy gap in the unperturbed HAMILTONian. An investigation of the analogue to the BRUECKNER ladder approximation then shows this to be free of the COOPER-type divergencies of the original BRUECKNER t-matrix provided only zero total momentum of the pairs is taken into account. This paper extends the investigation to non-vanishing total momentum. For a separable potential and weak interaction it is shown that there are no divergencies for any total momentum. The reason for this (as in the case of zero total momentum) is the existence of the energy gap in the unperturbed spectrum.
Abstract The structure of the Bogoljubov -Valatin transformation and the HFB state is investigated by group-theoretical methods. A direct proof of the Bloch-Messiah factorization theorem shows that the second factor which contains the BCS part of the BV transformation can be chosen always real. An unitary representation of the Bogoljubov-Valatin group in the Fock space is constructed which allows to write down various equivalent expressions for the HFB state vector. The relation between the "unitary form" and the usual form of | HFB〉 is clarified using the "quasispin" concept in connection with a theorem about the factorization of the D(3) Lie group.