HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 114 (2005) > Number 1
| Next Article >

Prog. Theor. Phys. Vol. 114 No. 1 (2005) pp. 57-75

[ Full Text PDF : FREE ACCESS (206K) ]

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

Constança Providência,1 João da Providência,1 Yasuhiko Tsue2 and Masatoshi Yamamura3

1Departamento de Fisica, Universidade de Coimbra, P-3000 Coimbra, Portugal
2Physics Division, Faculty of Science, Kochi University, Kochi 780-8520, Japan
3Faculty of Engineering, Kansai University, Suita 564-8680, Japan

(Received April 8, 2005)

Abstract:

Following the Schwinger boson representation for the su(M+1)- and su(N,1)-algebras 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 su(4)-algebras are studied. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high-temperature superconductivity.


URL : http://ptp.ipap.jp/link?PTP/114/57/
DOI : 10.1143/PTP.114.57

[ Full Text PDF : FREE ACCESS (206K) ] Citation:

References:

  1. H. J. Lipkin, N. Meshkov and A. Glick, Nucl. Phys. 62 (1965), 188[CrossRef].
  2. S. Y. Li, A. Klein and R. M. Dreizler, J. Math. Phys. 11 (1970), 975[CrossRef].
    F. Sakata, Y. Hashimoto, T. Marumori and T. Une, Prog. Theor. Phys. 70 (1983), 163[PTP].
    M. Matsuo and K. Matsuyanagi, Prog. Theor. Phys. 74 (1985), 288[PTP].
    K. Takada, Y. R. Shimizu and H. Thorn, Nucl. Phys. A 485 (1988), 189[CrossRef].
    M. Sambataro, Phys. Rev. C 60 (1999), 064320[APS].
  3. M. Yamamura, A. Kuriyama and T. Kunihiro, Prog. Theor. Phys. 104 (2000), 385[PTP]; ibid. 104 (2000), 401[PTP].
  4. J. P. Elliott, in Proceedings of International School of Physics ≪Enrico Fermi≫ Course XXXVI, ed. C. Bloch (Academic Press, New York and London, 1966), p. 128.
  5. M. Guidry, L.-A. Wu, Y. Sun and C.-L. Wu, Phys. Rev. B 63 (2001), 134516[APS].
    L.-A. Wu, M. Guidry, Y. Sun and C.-L. Wu, Phys. Rev. B 67 (2003), 014515[APS].
  6. S.-C. Zhang, Science 275 (1997), 1089[Science].
  7. A. Kuriyama, J. da Providência, Y. Tsue and M. Yamamura, Prog. Theor. Phys. 94 (1995), 1039[PTP]; ibid. 95 (1996), 339[PTP]; ibid. 96 (1996), 125[PTP].
    L. Brito, C. Providência and J. da Providência, Mod. Phys. Lett. A 12 (1999), 2985.
  8. J. da Providência, M. Yamamura and A. Kuriyama, Phys. Rev. C 50 (1994), 1720[APS].
    M. O. Terra, M. C. Nemes, C. Providência and J. da Providência, Ann. of Phys. 262 (1998), 1[CrossRef].
  9. S. T. Beliaev and V. G. Zelevinsky, Nucl. Phys. 39 (1962), 582[CrossRef].
  10. T. Marumori, M. Yamamura and A. Tokunaga, Prog. Theor. Phys. 31 (1964), 1009[PTP].
  11. A. Klein and E. R. Marshalek, Rev. Mod. Phys. 63 (1991), 375[APS].
    Special issue: International Conference on the Physics of Nuclear Structure of the Extremes (Lewes, Sussex, U. K. 17-19, June 1998), J. of Phys. G. 25 (1998), 577[CrossRef].
  12. A. Kuriyama, J. da Providência and M. Yamamura, Prog. Theor. Phys. 103 (2000), 285[PTP].
  13. J. Schwinger, in Quantum Theory of Angular Momentum, ed. L. C. Biedenharn and H. Van Dam (Academic Press, New York, 1955), p. 229.
  14. A. Kuriyama, C. Providência, J. da Providência, Y. Tsue and M. Yamamura, Prog. Theor. Phys. 105 (2001), 933[PTP].
  15. T. Holstein and H. Primakoff, Phys. Rev. 58 (1940), 1098[APS].
    S. C. Pang, A. Klein and R. M. Dreizler, Ann. of Phys. 49 (1968), 477[CrossRef].
  16. J. P. Elliott, Proc. R. Soc. London A 245 (1958), 128; ibid. 245 (1958), 562.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 115 No. 1 (2006) pp. 143-153 :
    Boson Realization of the su(3)-Algebra. I
    Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  2. Progress of Theoretical Physics Vol. 115 No. 1 (2006) pp. 155-164 :
    Boson Realization of the su(3)-Algebra. II
    Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  3. Progress of Theoretical Physics Vol. 115 No. 3 (2006) pp. 547-559 :
    Boson Realization of the su(3)-Algebra. III
    Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  4. Progress of Theoretical Physics Vol. 121 No. 6 (2009) pp. 1237-1287 :
    Many-Quark Model with su(4) Algebraic Structure
    Yasuhiko Tsue, Constança Providência, João da Providência and Masatoshi Yamamura

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.