Skip to main content
SpringerLink
Log in

The quantum group SU q (2), quasitriangularity, and application to theq-rotator model

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The quantum group structure of SU q (2) is described. The property of quasi triangularity and the Yang-Baxter equation are reviewed. A universalR-matrix for this algebra is written down. It is then shown in detail that this R-matrix satisfies the triangularity equations of Drinfeld and the Yang-Baxter equation given the algebraic SU q (2) commutation relations. In physical terms, the group can be realized as theq-rotator. A specific physical application to diatomic molecules is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Barbier, J. Meyer and M. Kibler, J. Phys. G20 (1994) L13.

    Google Scholar 

  2. R. Barbier, J. Meyer and M. Kibler, Int. J. Mod. Phys. 4 (1995) 385; R. Barbier and M. Kibler, in:Modern Group Theoretical Methods in Physics, eds. J. Bertrand et al. (Kluwer Academic Pub]., 1995) pp. 27–36.

    Google Scholar 

  3. V.G. Drinfeld,Proc. Int. Cong. Math. Amer. Math. Soc., Providence, RI (1987) p. 798.

  4. M. Kibler and T. Negadi, J. Math. Chem. 11 (1992)13.

    Google Scholar 

  5. R.B. Zhang, M.D. Gould and A.J. Bracken, Comm. Math. Phys. 137 (1991) 13.

    Google Scholar 

  6. M. Jimbo, Int. J. Mod. Phys. A4 (1989) 3759.

    Google Scholar 

  7. Z. Chang and H. Yen, Phys. Rev. A43 (1991) 6043.

    Google Scholar 

  8. M. Sweedler,Hopf Algebra (W.A. Benjamin, New York, 1969).

    Google Scholar 

  9. A.J. Bracken, D.S. McAnally, R.B. Zhang and M.D. Gould, J. Phys. A: Math. Gen. 24 (1991) 1379.

    Google Scholar 

  10. L.D. Landau and E.M Lifshitz,Quantum Mechanics, 3rd ed. (Pergamon Press, 1977).

  11. I. Dabrowski, Can. J. Phys. 62 (1984) 1639.

    Google Scholar 

  12. G. Herzberg,Molecular Spectra and Molecular Structure, I: Spectra of Diatomic Molecules, 2nd ed. (Van Nostrand, Princeton, 1955).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, N2L3G1, Waterloo, Ontario, Canada

    Paul Bracken

Authors
  1. Paul Bracken
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bracken, P. The quantum group SU q (2), quasitriangularity, and application to theq-rotator model. J Math Chem 19, 217–230 (1996). https://doi.org/10.1007/BF01166715

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01166715

Keywords

Search

Navigation