De Sitter to Poincaré contraction and relativistic coherent states
Ali, S. Twareque ; Antoine, J.-P. ; Gazeau, J.-P.
Annales de l'I.H.P. Physique théorique, Tome 52 (1990), p. 83-111 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1990__52_1_83_0,
     author = {Ali, S. Twareque and Antoine, J.-P. and Gazeau, Jean-Pierre},
     title = {De Sitter to Poincar\'e contraction and relativistic coherent states},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {52},
     year = {1990},
     pages = {83-111},
     mrnumber = {1046086},
     zbl = {0706.22018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1990__52_1_83_0}
}

Ali, S. Twareque; Antoine, J.-P.; Gazeau, J.-P. De Sitter to Poincaré contraction and relativistic coherent states. Annales de l'I.H.P. Physique théorique, Tome 52 (1990) pp. 83-111. http://gdmltest.u-ga.fr/item/AIHPA_1990__52_1_83_0/

[1] S.T. Ali and J.-P. Antoine, Ann. Inst. H. Poincaré, Vol. 50, 1989, n° 4.

[2] H. Bacry and J.M. Lévy-Leblond, J. Math. Phys., Vol. 9, 1968, p. 1605. | MR 238545 | Zbl 0162.58606

[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. | MR 34126

[4] E.P. Wigner, Ann. Math., Vol. 40, 1939, p. 149. V. Bargmann, Ann. Math., Vol. 59, 1954, p. 1.

[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. | MR 207913 | Zbl 0144.17202

[6] N. Ya. Vilenkin, Special Functions and the Theory of Group Representations, (Transl. RussianMath. Monographs, Vol. 22), Amer. Math. Soc., Providence, R.I., 1968. | MR 229863 | Zbl 0172.18404

[7] A. Perelomov, Generalized Coherent States and their Applications, Springer-Verlag, Berlin, 1986. | MR 899736 | Zbl 0605.22013

[8] T.O. Philips and E.P. Wigner, in Group Theory and its Applications, E. M. LOEBL Ed., Academic Press, New York, 1968. | MR 242432

[9] S. De Bièvre, J. Math. Phys., Vol. 30, 1989, p. 1401. | MR 1002242 | Zbl 0686.46049

[10] A.A. Kirillov, Elements of the Theory of Representations, Springer-Verlag, Berlin, 1976. | MR 412321 | Zbl 0342.22001

[11] H. Bacry and A. Kihlberg, J. Math. Phys., Vol. 10, 1969, p. 2132. | MR 263327 | Zbl 0191.27002

[12] R. Arens, Commun. Math. Phys., Vol. 21, 1971, pp. 125, 139, and J. Math. Phys., Vol. 12, 1971, p. 2415. | Zbl 0211.24402

[13] H. Bacry, Localizability and Space in Quantum Physics, (Lecture Notes in Physics, Vol. 308), Springer-Verlag, Berlin, 1988. | MR 957913 | Zbl 0653.53049

[14] B. Doubrovine, S. Novikov and A. Fomenko, Géométrie Contemporaine, Méthodes et Applications (Première partie), Mir, Moscou, 1982. | Zbl 0502.53002

[15] A. Unterberger andJ. Unterberger, Ann. Scient. Ec. Norm. Sup., Vol. 17, 1984, p. 83. | Numdam | Zbl 0549.35119

[16] R.L. Lipsman, Group Representations, (Lecture Notes in Mathematics, Vol. 388), Springer-Verlag, Berlin, 1974, | MR 372116 | Zbl 0283.22002

[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. | MR 55352 | Zbl 0050.02601

[18] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Square Integrability of Group Representations on Homogeneous Spaces I, II (in preparation).

[19] R. Balbinot, A. Elgradechi, J.-P. Gazeau and B. Giorgini, Phase Spaces for de Sitterian and Einsteinian Quantum Elementary Systems (in preparation).