Communications in Mathematical Physics

, Volume 21, Issue 1, pp 41–55 | Cite as

New “Coherent” States associated with non-compact groups

  • A. O. Barut
  • L. Girardello


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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    We use the notation in Barut, A. O., Fronsdal, C.: Proc. Roy. Soc. (London) Ser. A287, 532 (1965). This paper also contains the representations of the universal covering group. For a unified treatment ofSU (1, 1) andSU (2) see also Barut, A. O., Phillips, C.: Commun. Math. Phys.8, 52 (1968).Google Scholar
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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • A. O. Barut
    • 1
    • 2
  • L. Girardello
    • 1
    • 2
  1. 1.Institute of Theoretical PhysicsUniversity of ColoradoBoulder
  2. 2.Department of Physics and AstrophysicsUniversity of ColoradoBoulderUSA

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