New ’coherent’ states associated with non-compact groups. (English) Zbl 0214.38203


43A99 Abstract harmonic analysis
30D20 Entire functions of one complex variable (general theory)
Full Text: DOI


[1] Bargmann, V., Butera, P., Girardello, L., Klauder, J.R.: On the Completeness of the Coherent States (to be published).
[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). · Zbl 0132.27902
[3] Bateman Project: Vol. I. Integral transformations, p. 349. Erdelyi (editor). New York: McGraw-Hill 1954.
[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. · Zbl 0132.27902
[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. · Zbl 0050.02601
[6] Bargmann, V.: Commun. Pure Appl. Math.14, 187 (1961). · Zbl 0107.09102
[7] Segal, I. E.: Illinois J. Math.6, 500 (1962).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.