BOSON REPRESENTATION OF THE k-LEVEL LIPKIN MODEL

YANG Ya-Tian; YANG Yi; XU Gong-Ou

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2024年10月30日

Chinese Physics C> 1987, Vol. 11> Issue(4) : 505-514

BOSON REPRESENTATION OF THE k-LEVEL LIPKIN MODEL

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Abstract：
The boson representation of k-level Lipkin model for a fermion system was given by using the theory of coherent states. The method discussed in this paper can be used not only for the k-level Lipkin model corresponding to S_p (2k) group, but also for other solvable model corresponding to other semisimple Lie groups. It was pointed out that the norm operator is a function of the Casimir operators of dynamical group and its maximum stationary subgroup.

References

[1]

A. Bohr and B. R. Mottelson, Nuclear struczure, (W. A. Benjamin Inc. 1975).[2] J.M. Eisenberg and W. Greiner, Nuclear Models, (North Holland, Amsterdam 1970).[3] D. Jenssen, R. V. Jolos and F. Donau, Nucl. Phys, A224(1974), 93.[4] Xu Gong-ou, Nucl. Phys., A421(1984), 275c.[5] P.Ring and P. Scbuck, The nuclear many body problem (Springer Vcrlag, 1980), Chapter 9.[6] A. Arima and F. Iachllo, Phys. Rev. Lett., 35(1975), 1069; Ann. of Phys. ( N . Y.), 99(1976), 253; 111(1978), 201; 123(1979), 468.[7] R. Gilmore and D. H.. Feng, Progress in Panicle and Nuclear Physics, 9(1983), 479, R. Gilmorc, Liegroups, Lie algebras and some of their applications, (Wiley, New York, 1974).[8] J. Dobaczewski, Nucl. Phys, A369(1982), 213, 237, A380(1982), 1.[9] A. Klein, T. D. Cohen and C. T. Li, Ann. of Phys. (N. Y.), 141(1982), 382;A. Klein, H. Rafelski and J. Rafelski, Nucl. Phys, A355(1981), 189;T. D. Cohen and A. Klein, Nucl. Phys, A390(1982), 1.[10] Xu Gong-ou and Li Fuli, Commun. in Theor. Phys. (Beijing, China), 4(1985), 39.[11] J. Deenen and C. Quesne, J. Math. Phys, 23(1982), 878; 2004.[12] D. E. Littlewood, The theory of group characters, (Oxford University Press, Oxford 1950).[13] 万哲先, 李代数, (科学出版社,1978年).

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YANG Ya-Tian, YANG Yi and XU Gong-Ou. BOSON REPRESENTATION OF THE k-LEVEL LIPKIN MODEL[J]. Chinese Physics C, 1987, 11(4): 505-514.

YANG Ya-Tian, YANG Yi and XU Gong-Ou. BOSON REPRESENTATION OF THE k-LEVEL LIPKIN MODEL[J]. Chinese Physics C, 1987, 11(4): 505-514. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

BOSON REPRESENTATION OF THE k-LEVEL LIPKIN MODEL

Corresponding author: YANG Ya-Tian,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1987-08-05

Abstract: The boson representation of k-level Lipkin model for a fermion system was given by using the theory of coherent states. The method discussed in this paper can be used not only for the k-level Lipkin model corresponding to S_p (2k) group, but also for other solvable model corresponding to other semisimple Lie groups. It was pointed out that the norm operator is a function of the Casimir operators of dynamical group and its maximum stationary subgroup.