We show that a many-body Hamiltonian that corresponds to a system of fermions
interacting through a pairing force is an integrable problem, i.e. it has as
many constants of the motion as degrees of freedom. At the classical level this
implies that the Time-dependent Hartree-Fock- Bogoliubov dynamics is integrable
and at the quantum level that there are conserved operators of two-body
character which reduce to the number operators when the pairing strength
vanishes. We display these operators explicitly and study in detail the
three-level example.Comment: 14 pages, latex, 2 figures, to be published in Nuclear Physics
By introducing the concepts of quasi-spin pairing and quasi-spin seniority, the Lipkin model is extended to a variable number of particles. The properties of quasi-spin pairing are seen to be quite similar to those of ordinary pairing. The quasi-spin seniority allows one to obtain a simple classification of excited multiplets. A "pairing plus monopole" model is studied in connection with the Hartree-Fock theory.
An exactly soluble model for the study of projection techniques within the framework of the Hartree-Fock theory is presented. Properties of the exact solutions are analyzed and projections, both before and after variation, are discussed.
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