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Prog. Theor. Phys. Vol. 113 No. 1 (2005) pp. 153-168

On the Eigenvalue Problem of the su(1,1)-Algebra and the Coupling Scheme of Two su(1,1)-Spins

Seiya Nishiyama,¹ Constança Providência,² João da Providência,² Yasuhiko Tsue¹ and Masatoshi Yamamura³

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

(Received November 18, 2004)

Abstract:

After recapitulating the eigenvalue problem of the su(1,1)-algebra in the conventional form, the same problem is treated in an unconventional form, in which the eigenvalue is purely imaginary. Further, the coupling scheme of two su(1,1)-spins is discussed in the framework of two possibilities, in which certain new aspects appear. Finally, the coupling scheme developed in this paper is applied to a concrete example, which will serve boson realization of the so(4)- and so(3,1)-algebras presented in a subsequent paper.

URL : http://ptp.ipap.jp/link?PTP/113/153/
DOI : 10.1143/PTP.113.153

[ Full Text PDF : FREE ACCESS (174K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. A. Klein and E. R. Marshalek, Rev. Mod. Phys. 63 (1991), 375[APS].
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 (1981), 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. O. Terra, M. C. Nemes, C. Providência and J. da Providência, Ann. of Phys. 262 (1998), 1[CrossRef].
4. E. Celeghini, M. Rasetti, M. Tarlini and G. Vittiello, Mod. Phys. Lett. B 3 (1989), 1213.
   E. Celeghini, M. Rasetti and G. Vittiello, Ann. of Phys. 215 (1992), 156[CrossRef].
5. Y. Tsue, A. Kuriyama and M. Yamamura, Prog. Theor. Phys. 91 (1994), 49 [PTP]; ibid. 91 (1994), 469[PTP].
   A. Kuriyama, J. da Providência, Y. Tsue and M. Yamamura, Prog. Theor. Phys. Suppl. No. 141 (2001), 113[PTP].
6. A. Kuriyama, J. da Providência and M. Yamamura, Prog. Theor. Phys. 103 (2000), 285[PTP]; ibid. 103 (2000), 305[PTP].
   M. Yamamura, A. Kuriyama and T. Kunihiro, Prog. Theor. Phys. 104 (2000), 385 [PTP]; ibid. 104 (2000), 401[PTP].
   A. Kuriyama, C. Providência, J. da Providência, Y. Tsue and M. Yamamura, Prog. Theor. Phys. 109 (2003), 959[PTP].
7. A. Kuriyama, C. Providência, J. da Providência and M. Yamamura, Prog. Theor. Phys. 104 (2000), 143[PTP].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 113 No. 3 (2005) pp. 555-562 :

   A Note on the Eigenvalue Problem in the su(1,1)-Algebra

   Seiya Nishiyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura

2. Progress of Theoretical Physics Vol. 113 No. 3 (2005) pp. 563-580 :

   A Possible Boson Realization of the so(4)- and the so(3,1)-Algebra

   Seiya Nishiyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura

3. 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

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