New “Coherent” States associated with non-compact groups
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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- 1.Bargmann, V., Butera, P., Girardello, L., Klauder, J.R.: On the Completeness of the Coherent States (to be published).Google Scholar
- 2.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
- 3.Bateman Project: Vol. I. Integral transformations, p. 349. Erdelyi (editor). New York: McGraw-Hill 1954.Google Scholar
- 4.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.Google Scholar
- 5.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.Google Scholar
- 6.Bargmann, V.: Commun. Pure Appl. Math.14, 187 (1961).Google Scholar
- 7.Segal, I. E.: Illinois J. Math.6, 500 (1962).Google Scholar