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The Clebsch-Gordan coefficients for the covering of the (2 + 1)-Lorentz group in the parabolic basis

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  • Basu, Debabrata
  • Wolf, Kurt Bernardo

Abstract

We report on work in which we build the generalized oscillator algebra, an SO (2, 1) algebra of second-order differential operators with a specified domain, realizing all self-adjoint irreducible representations belonging to the discrete or the continuous series. The diagonal subalgebra of the direct sum of two such algebras leads to the definition of product and coupled states, whose inner product provides the Clebsch-Gordan coefficients. These are obtained as solutions to (multichart) Schrödinger equations for Pöschl-Teller potentials, which involve at most Gauss hypergeometric function 2F1.

Suggested Citation

  • Basu, Debabrata & Wolf, Kurt Bernardo, 1982. "The Clebsch-Gordan coefficients for the covering of the (2 + 1)-Lorentz group in the parabolic basis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 472-476.
  • Handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:472-476
    DOI: 10.1016/0378-4371(82)90335-1
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