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Symmetries in Science VIII pp 241–254Cite as

Some Aspects of q- and qp-Boson Calculus

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Abstract

The aim of the present paper is to continue the program of extending in the framework of q-deformations the main results of the work in ref. 1 on the SU2 unit tensor or Wigner operator (the matrix elements of which are coupling coefficients or 3 — jm symbols). A first part of this program was published in the proceedings of Symmetries in Science VI (see ref. 2) where the q-deformed Schwinger algebra was defined and where an algorithm, based on the method of complementary q-deformed algebras, was given for obtaining three-and four-term recursion relations for the Clebsch-Gordan coefficients (CGc’s) of Uq(su2) and Uq(su1,1). The algorithm was fully exploited in ref. 3 where the complementary of three quantum algebras in a q-deformation of the symplectic Lie algebra sp(8, ℝ) was used for producing 32 recursion relations.

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References

  1. M. Kibler and G. Grenet, J. Math. Phys. 21:422 (1980).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Yu.F. Smirnov and M.R. Kibler, Some aspects of q-boson calculus, in: Symmetries in Science VI: From the rotation group to quantum algebras, B. Gruber, ed., Plenum Press, New York (1993), p. 691.

    Google Scholar 

  3. M. Kibler, C. Campigotto and Yu.F. Smirnov, Recursion relations for Clebsch Gordan coefficients of Uq(su2) and Uq(su1,1), in: Proceedings of the International Workshop “Symmetry Methods in Physics, in Memory of Professor Ya.A. Smorodinsky”, A.N. Sissakian, G.S. Pogosyan and S.I. Vinitsky, eds., J.I.N.R., Dubna, Russia (1994), p. 246.

    Google Scholar 

  4. E. Wigner, Gruppentheorie and ihre Anwendungen auf die Quantenmechanik der Atomspektren, Vieweg & Sohn, Braunschweig (1931).

    Google Scholar 

  5. B.L. van der Waerden, Die Gruppentheoretische Methode in der Quantenmechanik, Springer, Berlin (1932).

    Google Scholar 

  6. G. Racah, Phys. Rev. 62:438 (1942).

    Article  ADS  Google Scholar 

  7. S.D. Majumdar, Prog. Theor. Phys. 20:798 (1958).

    Article  ADS  Google Scholar 

  8. A.P. Jucys and A.A. Bandzaitis, Theory of angular momentum in quantum mechanics, Mintis, Vilnius (1965).

    Google Scholar 

  9. L.C. Biedenharn and M. Tarlini, Lett. Math. Phys. 20:271 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. M. Nomura, J. Phys. Soc. Jpn. 59:1954 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  11. M. Nomura, J. Phys. Soc. Jpn. 59:2345 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  12. V.A. Groza, I.I. Kachurik and A.U. Klimyk, J. Math. Phys. 31:2769 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Yu.F. Smirnov, V.N. Tolstoi and Yu.I. Kharitonov, Sov. J. Nucl. Phys. 53:593 (1991).

    MathSciNet  Google Scholar 

  14. C. Quesne, q-bosons and irreducible tensors for q-algebras, in: Symmetries in Science VI: From the rotation group to quantum algebras, B. Gruber, ed., Plenum Press, New York (1993).

    Google Scholar 

  15. J. Shapiro, J. Math. Phys. 6:1680 (1965).

    Article  ADS  Google Scholar 

  16. J.-L. Calais, Int. J. Quantum Chem. 2:715 (1968).

    Article  ADS  Google Scholar 

  17. A.J. Macfarlane, J. Phys. A 22:4581 (1989).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. L.C. Biedenharn, J. Phys. A 22:L873 (1989).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. A. Sudbery, J. Phys. A: Math Gen. 23:L697 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. N. Reshetikhin, Lett. Math. Phys. 20:331 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. D.B. Fairlie and C.K. Zachos, Phys. Lett. B 256:43 (1991).

    Article  MathSciNet  ADS  Google Scholar 

  22. A. Schirrmacher, J. Wess and B. Zumino, Z. Phys. C 49:317 (1991).

    Article  MathSciNet  Google Scholar 

  23. S.T. Vokos, J. Math. Phys. 32:2979 (1991).

    Article  MathSciNet  ADS  Google Scholar 

  24. R. Chakrabarti and R. Jagannathan, J. Phys. A: Math. Gen. 24:L711 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. V.K. Dobrev, J. Math. Phys. 33:3419 (1992).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Yu.F. Smirnov and R.F. Wehrhahn, J. Phys. A: Math. Gen. 25:5563 (1992).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. M.R. Kibler, Introduction to quantum algebras, in: Symmetry and Structural Properties of Condensed Matter, W. Florek, D. Lipinski and T. Lulek, eds., World Scientific, Singapore (1993), p. 445.

    Google Scholar 

  28. S. Meljanac and M. Milekovie, J. Phys. A: Math. Gen. 26:5177 (1993).

    Article  ADS  MATH  Google Scholar 

  29. C. Quesne, Phys. Lett. A 174:19 (1993).

    Article  MathSciNet  ADS  Google Scholar 

  30. R. Chakrabarti and R. Jagannathan, J. Phys. A: Math. Gen. 27:2023 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. R. Barbier, J. Meyer and M. Kibler, J. Phys. G: Nucl. Part. Phys. 17:L67 (1994).

    Google Scholar 

  32. R. Barbier, J. Meyer and M. Kibler, A qp-rotor model for rotational bands of superdeformed nuclei, Preprint LYCEN 9437, IPNL (1994).

    Google Scholar 

  33. Ya.A. Smorodinskii and L.A. Shelepin, Usp. Fiz. Nauk 15:1 (1972).

    MathSciNet  Google Scholar 

  34. M. Kibler, G.-H. Lamot and Yu.F. Smirnov, to be published.

    Google Scholar 

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Author information

Author notes

  1. Yu. F. Smirnov

    Present address: Instituto de Física, Universidad Nacional Autonoma de México, México D.F. 001, México

Authors and Affiliations

  1. Institut de Physique Nucléaire de Lyon, IN2P3-CNRS et Université Claude Bernard, 43 Boulevard du 11 Novembre 1918, F-69622, Villeurbanne Cedex, France

    M. R. Kibler & R. M. Asherova

  2. Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia

    Yu. F. Smirnov

Authors
  1. M. R. Kibler
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  2. R. M. Asherova
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  3. Yu. F. Smirnov
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Editor information

Editors and Affiliations

  1. Southern Illinois University at Carbondale in Niigata, Niigata, Japan

    Bruno Gruber

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Kibler, M.R., Asherova, R.M., Smirnov, Y.F. (1995). Some Aspects of q- and qp-Boson Calculus. In: Gruber, B. (eds) Symmetries in Science VIII. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1915-7_18

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  • DOI: https://doi.org/10.1007/978-1-4615-1915-7_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5783-4

  • Online ISBN: 978-1-4615-1915-7

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