A group theoretical method for calculating overlaps of HFB states

Overlaps of Hartree-Fock-Bogoljubov states occurring in modified HFB theories (e. g. projected HFB) are calculated using group theoretical methods. For this purpose the Bogoliubov-Valatin transformation is generalized. The resulting nonunitary transformation leaves the Fermi commutation relations invariant, but the characteristic property of the creation and annihilation operators, namely that they are hermitean conjugate to each other, is lost. A suitable factorization of the new transformation is derived, which also applies to the unitary Bogoliubov-Valatin transformation but the structure of which is completely different from the well-known Bloch-Messiah decomposition. Furthermore, the relation between various representations of the HFB state vector is clarified.