Quantum mechanics and coherent states on the anti-de Sitter spacetime and their Poincaré contraction
De Bièvre, Stephan ; El Gradechi, Amine M.
Annales de l'I.H.P. Physique théorique, Tome 56 (1992), p. 403-428 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1992__57_4_403_0,
     author = {De Bi\`evre, Stephan and El Gradechi, Amine M.},
     title = {Quantum mechanics and coherent states on the anti-de Sitter spacetime and their Poincar\'e contraction},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {56},
     year = {1992},
     pages = {403-428},
     mrnumber = {1198985},
     zbl = {0770.53048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1992__57_4_403_0}
}

De Bièvre, Stephan; El Gradechi, Amine M. Quantum mechanics and coherent states on the anti-de Sitter spacetime and their Poincaré contraction. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) pp. 403-428. http://gdmltest.u-ga.fr/item/AIHPA_1992__57_4_403_0/

[AAG] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, De Sitter to Poincaré Contraction and Relativistic Coherent States, Ann. Inst. Henri Poincaré, Vol. 52, 1, 1990, pp. 83-111. | Numdam | MR 1046086 | Zbl 0706.22018

[AM] R. Abraham and J. Marsden, Foundations of mechanics, 2nd Ed., Benjamin/ Cummings, Mass., 1978. | MR 515141 | Zbl 0393.70001

[BEGG] R. Balbinot, M.A. El Gradechi, J.-P. Gazeau and B. Giorgini, Phase spaces for quantum elementary systems in de Sitter and Minkowski spacetimes, Preprint L.P. T.M., 1990.

[BLL] H. Bacry and J.M. Lévy-Leblond, Possible kinematics, J.M.P., Vol. 9, 1968, pp. 1605-1614. | MR 238545 | Zbl 0162.58606

[CDB] C. Cishahayo and S. De Bièvre, On the contraction of the discrete series of SU(1, 1), Ann. Inst. Fourier (to appear). | Numdam | Zbl 0793.22005

[D] A.H. Dooley, Contractions of Lie groups and applications to analysis; in Topics in modern harmonic analysis, Proceedings of a seminar held in Torino and Milano, May-June 1982, Vol. I, pp.483-515, Instituto Nazionale di Alta Matematica Francesco Severi, Roma, 1983. | MR 748872 | Zbl 0551.22006

[DB] S. De Bièvre, Scattering in relativistic particle mechanics, Ph. D. Thesis, Dept. of Physics, University of Rochester, 1986.

[EDB] M.A. El Gradechi and S. De Bièvre, Phase space quantum mechanics on the Anti-de Sitter spacetime, and its Poincaré contraction, preprint CRM-1838, hepth- 9210133, 1992.

[DBEG] S. De Bièvre, M.A. El Gradechi and J.-P. Gazeau, Phase space description of a quantum elementary system on the anti-de Sitter spacetime and its contraction, Proceedings of the 18th International Colloquium on Group Theoretical Methods in Physics, Moscow 4-9 June 1990 (to appear).

[F] C. Fronsdal, Elementary particles in a curved space I, II, III and IV, Rev. Mod. Phys., 37, 1965, pp.221-224; Phys. Rev. D., Vol. 10, 1974, pp. 589-598; Phys. Rev. D, Vol. 12, 1975, pp. 3810-3818; Phys. Rev. D, Vol. 12, 1975, pp. 3819-3830. | MR 178939

[FF] M. Flato and C. Fronsdal, Three-dimensional Singletons, Lett. Math. Phys., Vol. 20, 1990, pp.65-74. | MR 1058996 | Zbl 0697.53083

[GH] J.-P. Gazeau and M. Hans, Integral spin fields on (3 + 2)-de Sitter space, J.M.P., Vol. 29, 1988, pp. 2533-2552. | MR 969703 | Zbl 0783.53048

[IW] E. Inönu and E.P. Wigner, On the contraction of groups and their representations, Proc. Nat. Acad. Sci. U.S.A., Vol. 39, 1953, pp. 510-524. | MR 55352 | Zbl 0050.02601

[LN] M. Lévy-Nahas, Deformation and contraction of Lie algebras, J.M.P., Vol. 8, 1967, pp. 1211-1222. | MR 224747 | Zbl 0175.24803

[MN] J. Mickelsson and J. Niederle, Contractions of representations of de Sitter groups, C.M.P., Vol. 27, 1972, pp. 167-180. | MR 309502 | Zbl 0236.22021

[Pe] A. Perelomov, Generalized coherent states and their applications, Springer Verlag, Berlin, 1986. | MR 899736 | Zbl 0605.22013

[R] J.H. Rawnsley, De Sitter symplectic spaces and their quantizations, Proc. Camb. Phil. Soc., Vol. 76, 1974, pp. 473-480. | MR 353853 | Zbl 0286.22017

[S] E.J. Saletan, Contraction of Lie groups, J.M.P., Vol. 2, 1961, pp. 1-21. | MR 127213 | Zbl 0098.25804

[Sn] J. Sniatycki, Dirac brackets in geometric dynamics, Ann. Inst. H. Poincaré, Vol. 20, 1974, pp. 365-372. | Numdam | MR 358860 | Zbl 0295.70010

[So] J.M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970. | MR 260238 | Zbl 0186.58001

[W] N. Woodhouse, Geometric quantization, Clarendon Press, Oxford, 1980. | MR 605306 | Zbl 0458.58003