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##### Background of the $su(2)$-Algebraic Many-Fermion Models in the Boson Realization

**Authors**: Yasuhiko Tsue, Constança Providência, João da Providência, Masatoshi Yamamura

**Ref.**: Progress of Theoretical Physics **127**, 117-143 (2012)

**Abstract**: The su(2)-algebraic many-fermion model is formulated so as to be able to get the unified understanding of the structures of three simple models: the single-level pairing, the isoscalar proton-neutron pairing and the two-level Lipkin model. The basic idea is to introduce an auxiliary su(2)-algebra, any generator of which commutes with any generator of the starting su(2)-algebra. With the aid of this algebra, the minimum weight states are completely determined in simple form. Further, concerning the two algebras, boson realization is presented. Through this formulation, the behavior of the total fermion in the Lipkin model is notably different from that in the other two models. As the supplementary problem, the boson-fermion realization and the Lipkin model in the isovector pairing model are investigated.

**DOI**: 10.1143/PTP.127.117