International Journal of Theoretical Physics

, Volume 33, Issue 6, pp 1229–1235 | Cite as

The quantum groupSUq(2) andq-analog of angular momentum operators in quantum mechanics

  • Shengli Zhang
  • Yishi Duan


We present three operators in quantum mechanics that obey the commutation relations of quantum groupSUq(2). These operators are nonlinear combinations of the conventional angular momentum operators and are called the quantumq-analog angular momentum operators. When the quantum deformation parameterr = Inq vanishes, these quantumq-analog angular momentum operators reduce to the usual angular momentum operators.


Field Theory Angular Momentum Elementary Particle Quantum Field Theory Quantum Mechanic 
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  1. Alvarez-Gaume, L., Gomez, C., and Sierra, G. (1989).Physics Letters B,220, 142.Google Scholar
  2. Baxter, R. J. (1972).Annals of Physics,1, 193.Google Scholar
  3. Baxter, R. J. (1982).Exactly Solved Model in Statistical Mechanics, Academic Press, New York.Google Scholar
  4. Biedenharn, L. C. (1989).Journal of Physics A Mathematical and General,22, L873.Google Scholar
  5. Biedenharn, L. C., and Louck, J. D. (1981). Angular momentum in quantum physics, inEncyclopedia of Mathematics and Its Applications, Addison-Wesley, Reading, Massachusetts, Vol. 8.Google Scholar
  6. Chaichian, M., Kulish, P., and Lukierski, J. (1990).Physics Letters B,237, 401.Google Scholar
  7. Drinfeld, V. G. (1986). Quantum groups, inProceedings International Congress of Mathematics, MSRI, Berkeley, p. 798.Google Scholar
  8. Drinfeld, V. G. (1988).Soviet Mathematics Doklady,36, 212.Google Scholar
  9. Faddeev, L. (1984). InIntegrable Models in (1+1)-Dimensional Quantum Field Theory (Les Houches XXXIX), J.-B. Zuber and R. Stora, eds., Elsevier, Amsterdam, Course 8.Google Scholar
  10. Frohlich, J. (1987). InStatistics of Fields, the Yang — Baxter Equations, and Theory of Knots and Links, A. Jaffeet al., eds., Plenum Press, New York.Google Scholar
  11. Jimbo, M. (1985).Letters in Mathematical Physics,10, 63.Google Scholar
  12. Jimbo, M. (1986a).Letters in Mathematical Physics,102, 247.Google Scholar
  13. Jimbo, M. (1986b).Communications in Mathematical Physics,102, 537.Google Scholar
  14. Kulish, P., and Damashinsky, E. (1990).Journal of Physics A Mathematical and General,23, L415.Google Scholar
  15. Macfarlane, A. J. (1989).Journal of Physics A Mathematical and General,22, 4581.Google Scholar
  16. Qian, B. C., and Zeng, J. Y. (1988).An Analysis of Problems in Quantum Mechanics, Science Press, Beijing [in Chinese].Google Scholar
  17. Schiff, L. I. (1968).Quantum Mechanics, McGraw-Hill, New York.Google Scholar
  18. Sun, C. P., and Fu, H. C. (1989).Journal of Physics A Mathematical and General,22, L983.Google Scholar
  19. Yang, C. N. (1968).Physical Review,170, 1591.Google Scholar
  20. Zamolodchikov, A. B., and Zamolodchikov, A. B. (1979).Annals of Physics,120, 253.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Shengli Zhang
    • 1
  • Yishi Duan
    • 1
  1. 1.Division of Theoretical Physics, Department of PhysicsLanzhou UniversityLanzhou, GansuChina

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