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The Clebsch-Gordan coefficients ofsl(2,R) in the parabolic basis

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Czechoslovak Journal of Physics B Aims and scope

Abstract

We realize the Lie algebra sl(2,R) in terms of second-order differential operators defined on a dense common domain of square-integrable functions on a two-chart space, where the self-adjoint extension(s) (families) lead to all (and only) self-adjoint irreducible representations of the algebra, single- as well as multi-valued over the group. This allows for a rather straight-forward evaluation of the Clebsch-Gordan coefficients of sl(2,R) in the parabolic subalgebra basis.

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology, Kharagpur, India

    D. Basu

  2. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de Mexico, México D. F., México

    K. B. Wolf

Authors
  1. D. Basu
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  2. K. B. Wolf
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Additional information

I would like to thank the hospitality of Prof. J. A. de Azcárraga, at the Instituto de Fí'sica Teórica, Universidad de Valencia, where this review was written.

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Basu, D., Wolf, K.B. The Clebsch-Gordan coefficients ofsl(2,R) in the parabolic basis. Czech J Phys 32, 584–588 (1982). https://doi.org/10.1007/BF01596850

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  • DOI: https://doi.org/10.1007/BF01596850

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