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

43A99Miscellaneous topics in harmonic analysis
30D20General theory of entire functions
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 · doi:10.1098/rspa.1965.0195
[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 · doi:10.1098/rspa.1965.0195
[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 · doi:10.1073/pnas.39.6.510
[6] Bargmann, V.: Commun. Pure Appl. Math.14, 187 (1961). · Zbl 0107.09102 · doi:10.1002/cpa.3160140303
[7] Segal, I. E.: Illinois J. Math.6, 500 (1962).