International Journal of Theoretical Physics

, Volume 44, Issue 8, pp 1217–1225 | Cite as

Yangian Realization for Dirac Oscillator



We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operators for different energy levels for this system are obtained.


Yangian Dirac oscillator shift operators 


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  1. Baxter, R. J. (1982). Exactly Solved Models in Statistical Mechanics, London. Academic Press.Google Scholar
  2. Cook, P. A. (1971). Letters Nuovo Cimento 1, 419.Google Scholar
  3. Delange, O. L. (1991). Journal of Mathematical Physics 32(5), 1296.MathSciNetADSGoogle Scholar
  4. Drinfeld, V. G. (1985). Soviet Mathematical Doklady 32, 254; Drinfeld, V. G. (1986). Quantum Group In: Proceedings of ICM. Berkeley (California). Academic Press, 269; Drinfeld, V. G. (1988). Soviet Mathematical Doklady 36, 212.Google Scholar
  5. Ge, M. L. and Xue, K. (1999). Yang-Baxter Equation, Shanghai. Technical Education Press.Google Scholar
  6. Ge, M. L., Cho, Y. M., and Xue, K. (1999). Physics Letters 260A, 484; Ba, C. M., Ge, M. L., and Xue, K. (2001). Journal of Statistical Physics 102, 545; Ge, M. L., Kwek, L. C., Liu, Y., Oh, C. H., and Wang, X. B. (2000). Physics Review 62A, 052110.Google Scholar
  7. Itô, D., Mori, K., and Carriere, E. (1967). Nuovo Cimento 51A, 1119.Google Scholar
  8. Moshinsky, M. and Szczepaniak, A. (1989). Journal of Physics A: Mathemaical and General 22, L817.MathSciNetADSGoogle Scholar
  9. Quesne, C. and Moshinsky, M. J. (1990). Physics A: Mathematical and General 23, 2263.MathSciNetADSGoogle Scholar
  10. Yang, C. N. (1967). Physics Review Letters 19, 1312.MATHADSGoogle Scholar

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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of PhysicsNational University of SingaporeSingapore
  2. 2.Department of PhysicsNortheast Normal UniversityChangchunP. R. China
  3. 3.Department of PhysicsNational University of SingaporeSingapore

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