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Some Aspects of q- and qp-Boson Calculus

In: Symmetries in Science VIII

Author

Listed:
  • M. R. Kibler

    (IN2P3-CNRS et Université Claude Bernard, Institut de Physique Nucléaire de Lyon)

  • R. M. Asherova

    (IN2P3-CNRS et Université Claude Bernard, Institut de Physique Nucléaire de Lyon)

  • Yu. F. Smirnov

    (Moscow State University, Institute of Nuclear Physics)

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.

Suggested Citation

  • M. R. Kibler & R. M. Asherova & Yu. F. Smirnov, 1995. "Some Aspects of q- and qp-Boson Calculus," Springer Books, in: Bruno Gruber (ed.), Symmetries in Science VIII, pages 241-254, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1915-7_18
    DOI: 10.1007/978-1-4615-1915-7_18
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