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Nuclear Physics A

Generalization of the quantized Bogoliubov-Valatin transformation and relation to the method of the vector coherent state: The case of U(3)

Abraham Klein, Niels R. Walet

Published Aug 1, 1990• 5 citations
Publisher
DOI
10.1016/0375-9474(90)90366-t

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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 BogoliubovValatin 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. (GE)

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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.
The new method presented by B. Bremond and J. G. Valatin is generalized which at-tache ~ four body correlation to the Bogoliubov transformation. The generalization carried in this paper is similar to that from the Bogoliubov transformation to the generalized Bogoliubov one. We find a criterion of whether a trial ground state vector has an essential feature of four body correlation or it is like that of the generalized Bogoliubov transformation. This method is applied to a system with a charge independent pairing interaction. There appear two. different kinds of single quasiparticle excitation energy due to proton-neutron interaction.
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 BogoliubovValatin 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. (GE)