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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bargmann, V., Butera, P., Girardello, L., Klauder, J.R.: On the Completeness of the Coherent States (to be published).
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).
Bateman Project: Vol. I. Integral transformations, p. 349. Erdelyi (editor). New York: McGraw-Hill 1954.
Barut, A. O., Phillips, C.: Cited in Ref. 2; ; Mukunda, M.: J. Math. Phys.8, 2210 (1967); Lindblad, G., Nagel, B.: Stockholm preprint, April 1969. See also Vilenkin, N. J.: Special functions and the theory of group representations, Chapt. VII. Providence, Rhode Island: American Mathematical Society 1968.
Inönü, E., Wigner, E. P.: Proc. Natl. Acad. Sci. U.S.39, 510 (1953). Inönü, E.: In: Group theoretical concepts and methods in elementary particle physics, ed. by F. Gürsey. New York: Gordon and Breach 1964.
Bargmann, V.: Commun. Pure Appl. Math.14, 187 (1961).
Segal, I. E.: Illinois J. Math.6, 500 (1962).
Author information
Authors and Affiliations
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).
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01646483