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New “Coherent” States associated with non-compact groups

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Abstract

Generalized “Coherent” States are the eigenstates of the lowering and raising operators of non-compact groups. In particular the discrete series of representations ofSO (2, 1) are studied in detail: the resolution of the identity and the connection with the Hilbert spaces of entire functions of growth (1, 1). Also discussed are the application to the evaluation of matrix elements of finite group elements and the contraction to the usual coherent states.

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References

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Colorado, Boulder, Colorado

    A. O. Barut & L. Girardello

  2. Department of Physics and Astrophysics, University of Colorado, 80302, Boulder, Col., USA

    A. O. Barut & L. Girardello

Authors
  1. A. O. Barut
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  2. L. Girardello
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Additional information

Supported in part by the Air Force Office of Scientific Research under Grant AF-AFOSR-30-67.

On leave from Istituto di Fisica dell'Universitá, Parma and Istituo Nazionale di Fisica Nucleare, Sezione di Milano (Italy).

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Barut, A.O., Girardello, L. New “Coherent” States associated with non-compact groups. Commun.Math. Phys. 21, 41–55 (1971). https://doi.org/10.1007/BF01646483

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  • DOI: https://doi.org/10.1007/BF01646483

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