De Sitter to Poincaré contraction and relativistic coherent states

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1. [1] S.T. Ali and J.-P. Antoine, Ann. Inst. H. Poincaré, Vol. 50, 1989, n° 4. 
2. [2] H. Bacry and J.M. Lévy-Leblond, J. Math. Phys., Vol. 9, 1968, p. 1605. Zbl0162.58606MR238545
3. [3] E.P. Wigner, Proc. Nat. Acad. Sci. U.S.A., Vol. 36, 1950, p. 184. C. Fronsdal, Rev. Mod. Phys., Vol. 37, 1965, p. 221. J.-P. Gazeau and M. Hans, J. Math. Phys., Vol. 29, 1988, p. 2533. MR34126
4. [4] E.P. Wigner, Ann. Math., Vol. 40, 1939, p. 149. V. Bargmann, Ann. Math., Vol. 59, 1954, p. 1. 
5. [5] I.M. Gel'fand, M.I. Graev and N. Ya. Vilenkin, Generalized Functions, Vol. 5, Integral Geometry and Representation Theory, Academic Press, N. Y., 1966. Zbl0144.17202MR207913
6. [6] N. Ya. Vilenkin, Special Functions and the Theory of Group Representations, (Transl. RussianMath. Monographs, Vol. 22), Amer. Math. Soc., Providence, R.I., 1968. Zbl0172.18404MR229863
7. [7] A. Perelomov, Generalized Coherent States and their Applications, Springer-Verlag, Berlin, 1986. Zbl0605.22013MR899736
8. [8] T.O. Philips and E.P. Wigner, in Group Theory and its Applications, E. M. LOEBL Ed., Academic Press, New York, 1968. MR242432
9. [9] S. De Bièvre, J. Math. Phys., Vol. 30, 1989, p. 1401. Zbl0686.46049MR1002242
10. [10] A.A. Kirillov, Elements of the Theory of Representations, Springer-Verlag, Berlin, 1976. Zbl0342.22001MR412321
11. [11] H. Bacry and A. Kihlberg, J. Math. Phys., Vol. 10, 1969, p. 2132. Zbl0191.27002MR263327
12. [12] R. Arens, Commun. Math. Phys., Vol. 21, 1971, pp. 125, 139, and J. Math. Phys., Vol. 12, 1971, p. 2415. Zbl0211.24402
13. [13] H. Bacry, Localizability and Space in Quantum Physics, (Lecture Notes in Physics, Vol. 308), Springer-Verlag, Berlin, 1988. Zbl0653.53049MR957913
14. [14] B. Doubrovine, S. Novikov and A. Fomenko, Géométrie Contemporaine, Méthodes et Applications (Première partie), Mir, Moscou, 1982. Zbl0502.53002
15. [15] A. Unterberger and J. Unterberger, Ann. Scient. Ec. Norm. Sup., Vol. 17, 1984, p. 83. Zbl0549.35119
16. [16] R.L. Lipsman, Group Representations, (Lecture Notes in Mathematics, Vol. 388), Springer-Verlag, Berlin, 1974, Zbl0283.22002MR372116
17. [17] E. Inönü and E.P., Wigner, Proc. Nat. Acad. Sci. U.S.A., Vol, 39, 1953, p. 510. E. Inönü, in Group Theoretical Concepts and Methods in Elementary Particle Physics, F. GÜRSEY Ed,, p, 365, Gordon and Breach, N. Y., 1964. Zbl0050.02601MR55352
18. [18] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Square Integrability of Group Representations on Homogeneous Spaces I, II (in preparation). Zbl0752.22002
19. [19] R. Balbinot, A. Elgradechi, J.-P. Gazeau and B. Giorgini, Phase Spaces for de Sitterian and Einsteinian Quantum Elementary Systems (in preparation). 

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