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The Lipkin Model in the su(M+1)-Algebra for Many-Fermion System and its Counterpart in the Schwinger Boson Representation

C. Providencia·J. da Providencia·Y. Tsue·M. Yamamura
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Abstract

Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators such as the particle-hole pairs are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and the su(4)-algebra are discussed. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high temperature superconductivity.

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C. Providencia, J. da Providencia, Y. Tsue, M. Yamamura. 2005-04-08. The Lipkin Model in the su(M+1)-Algebra for Many-Fermion System and its Counterpart in the Schwinger Boson Representation. https://doi.org/10.1143/ptp.114.57

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