Some Aspects of q- and qp-Boson Calculus

M. R. Kibler, R. M. Asherova and Yu. F. Smirnov
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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

A chapter in Symmetries in Science VIII, 1995, pp 241-254 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4615-1915-7_18

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