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Some Aspects of q- and qp-Boson Calculus

  • M. R. Kibler
  • R. M. Asherova
  • Yu. F. Smirnov

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.

Keywords

Commutation Relation Hopf Algebra Recursion Relation Intermediate Form Quantum Algebra 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • M. R. Kibler
    • 1
  • R. M. Asherova
    • 1
  • Yu. F. Smirnov
    • 2
  1. 1.Institut de Physique Nucléaire de LyonIN2P3-CNRS et Université Claude BernardVilleurbanne CedexFrance
  2. 2.Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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