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

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

2011-08-30

arxiv.org/abs/1108.5816v1

Prog. Theor. Phys. 127 (2012), 117-143

Physics

Nuclear Physics

Nuclear Theory

27 pages, 1 figure, using PTPTeX class

Scientific paper

10.1143/PTP.127.117

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. 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 a simple forms. 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 of those in the other two models. As supplementary problem, the boson-fermion realization and the Lipkin model in the isovector pairing model are investigated.

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