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Background of the su(2)-Algebraic Many-Fermion Models in the Boson Realization Construction of Minimum Weight States by Means of an Auxiliary su(2)-Algebra and its Related Problems

Y. Tsue, Masatoshi Yamamura

Published Jan 1, 2013• 2 citations
OpenAlex

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The role of the auxiliary su(2)-algebra proposed by the present authors in the latest paper is extended. Its aim is to determine the minimum weight states completely. With the aid of scalar operators for the auxiliary algebra, new aspects are added to the minimum weight states in the aligned scheme discussed in the latest paper. Some simple examples are shown.

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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.