Abstract
In this paper two kinds of two-boson realizations of the polynomial angular momentum algebra are obtained by generalizing the well known Jordan–Schwinger realizations of the SU(2) and SU(1,1) algebras. Especially, for the Higgs algebra, an unitary realization and two nonunitary realizations, together with the properties of their respective acting spaces are discussed in detail. Furthermore, similarity transformations, which connect the nonunitary realizations with the unitary ones, are gained by solving the corresponding unitarization equations. As applications, the dynamical symmetry of the Kepler system in a two-dimensional curved space is studied and phase operators of the Higgs algebra are constructed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Condon E.U., Odabasi H. (1980). Atomic Structure. Cambridge University, New York
Klein A., Marshalek E.R. (1991). Rev. Mod. Phys. 63: 375
Halonen L., Child M.S. (1983). J. Chem. Phys. 79: 559
Iachello F. (1995). Algebraic Theory of Molecules. Oxford University, New York
Biedenharn L.C., Louck J.D. (1981). Angular Momentum in Quantum Physics. Addison-Wesley, Reading, Massachusetts
J. Schwinger, in: The Quantum Physics of Angular Momentum, eds. L.C. Biedenharn and H. Van Dam (Academic, New York, 1965)
Roček M. (1991). Phys. Lett. B255: 554
Higgs P.W. (1979). J. Phys. A12: 309
Zhedanov A.S. (1992). Mod. Phys. Lett. A7: 507
Jimbo M. (1985). Lett. Math. Phys. 10: 63
Daskaloyannis C. (1991). J. Phys. A24: L789
Bonatsos D., Daskaloyannis C., Kokkotas K. (1994). Phys. Rev. A50: 3700
Bonatsos D., Kolokotronis P., Daskaloyannis C. (1995). Mod. Phys. Lett. A10: 2197
Quesne C. (1994). Phys. Lett. A193: 245
Junker G., Roy P. (1999). Phys. Lett. A257: 113
Sunilkumar V., Bambah B.A., Jagannathan R., Panigrah P.K., Srinivasan V. (2000). J. Opt. B2: 126
V. Sunilkumar, B.A. Bambah and R. Jagannathan, arXiv: math-ph/0205005
Beckers J., Brihaye Y., Debergh N. (1999). J. Phys. A32: 2791
Debergh N. J. Phys. A31 (1998) 4013. ibid. A33 (2000) 7109
Ruan D., Wang F., Tu C.C., Sun H.Z. (2000). Commun. Theor. Phys. 34: 643
D. Ruan, in: Recent Progress in Quantum Mechanics, eds. J.Y. Zeng, S.Y. Pei and G.L. Long (Peking University, Beijing, 2001)
Holstein T., Primakoff H. (1940). Phys. Rev. 58: 1098
Dyson J.F. (1956). Phys. Rev. 102: 1217
Ruan D. (2003). Phys. Lett. A319: 122
Iachello F. (1993). Rev. Mod. Phys. 65: 569
W. Pauli, Z. Phys. 36 (1926) 336; V. A. Fock, Z. Phys. 98 (1935) 145; V. Bargmann, Z. Phys. 99 (1936) 576
Dirac P.A.M. (1923). Proc. Roy. Soc. (London) A114: 243
Susskind L., Glogower J. (1964). Physics. 1: 49
Carruthers P., Nieto M.M. (1968). Rev. Mod. Phys. 40: 411
Fan H.Y., Li Y.P. (1988). Commun. Theor. Phys. 9: 341
Man’ko V.I., Marmo G., Sudarshan E.C.G., Zaccaria F. (1997). Phys. Scr. 55: 528
de Matos R.L., Vogel W. (1996). Phys. Rev. A54: 4560
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ruan, D. Two-boson Realizations of the Polynomial Angular Momentum Algebra and Some Applications. J Math Chem 39, 417–440 (2006). https://doi.org/10.1007/s10910-005-9025-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-005-9025-1