@article{AIHPA_1991__55_4_857_0, author = {Ali, S. T. and Antoine, J.-P. and Gazeau, J.-P.}, title = {Square integrability of group representations on homogeneous spaces. {II.} {Coherent} and quasi-coherent states. {The} case of the {Poincar\'e} group}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {857--890}, publisher = {Gauthier-Villars}, volume = {55}, number = {4}, year = {1991}, mrnumber = {1144105}, zbl = {0752.22003}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1991__55_4_857_0/} }
TY - JOUR AU - Ali, S. T. AU - Antoine, J.-P. AU - Gazeau, J.-P. TI - Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group JO - Annales de l'I.H.P. Physique théorique PY - 1991 SP - 857 EP - 890 VL - 55 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1991__55_4_857_0/ LA - en ID - AIHPA_1991__55_4_857_0 ER -
%0 Journal Article %A Ali, S. T. %A Antoine, J.-P. %A Gazeau, J.-P. %T Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group %J Annales de l'I.H.P. Physique théorique %D 1991 %P 857-890 %V 55 %N 4 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1991__55_4_857_0/ %G en %F AIHPA_1991__55_4_857_0
Ali, S. T.; Antoine, J.-P.; Gazeau, J.-P. Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group. Annales de l'I.H.P. Physique théorique, Volume 55 (1991) no. 4, pp. 857-890. http://archive.numdam.org/item/AIHPA_1991__55_4_857_0/
[1] Square Integrability of Group Representations on Homogeneous Spaces I. Reproducing Triples and Frames, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 55, 1991, pp. 829-855. | Numdam | MR | Zbl
, and ,[2] Generalized Coherent States and their Applications, Springer-Verlag, Berlin, 1986. | MR | Zbl
,[3] Coherent States. Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985. | MR | Zbl
and ,[4] J. Math. Phys., Vol. 30, 1989, p. 1401.
,[5] Trans. Am. Math. Soc., Vol. 72, 1952, p. 341. | MR | Zbl
and ,[6] J: Math. Phys., Vol. 27, 1986, p. 1271. | MR | Zbl
, and ,[7] Ann. Inst. H. Poincaré, Phys. Théor., Vol. 51, 1989, p. 23. | Numdam | MR | Zbl
and ,[8] Ann. Inst. H. Poincaré, Phys. Théor., Vol. 52, 1990, p. 83. | Numdam | MR | Zbl
, and ,[9] Geometry of Quantum Theory. Vol. II. Quantum Theory of Covariant Systems, Van Nostrand Rheinhold, New York, 1970. | MR | Zbl
,[10] J. Math. Phys., Vol. 21, 1980, p. 2719. | MR | Zbl
, and ,[11] Proc. Nat. Acad. Sci. (U.S.A.), Vol. 35, 1949, p. 537. | MR | Zbl
,[12] Les C*-algèbres et leurs représentations, 2e éd., Gauthier-Villars, Paris, 1969. | MR | Zbl
,[13] J. Math. Phys., Vol. 26, 1985, p. 2473. | MR | Zbl
, and ,[14] Helv. Phys. Acta, Vol. 56, 1983, p. 1140.
and ,[15] J. Math. Phys., Vol. 22, 1981, p. 2389. | MR
,[16] Lett. Math. Phys., Vol. 5, 1981, p. 161. | MR | Zbl
,[17] Acta Appl. Math., Vol. 6, 1986, p. 19. | MR | Zbl
and ,[18] Acta Appl. Math., Vol. 6, 1986, p. 47. | Zbl
and ,[19] J. Math. Phys., Vol. 32, 1991, p. 1273; Time-Frequency Representations: Wavelet Packets and Optimal Decomposition, Ann. Inst. H. Poincaré, Phys. Théor. (to appear). | Numdam | Zbl
,[20] J. Math. Phys., Vol. 19, 1978, p. 2260.
,[21] J. Math. Phys., Vol. 18, 1977, p. 952; Vol. 19, 1978, p. 502.
,[22] J. Math. Phys., Vol. 18, 1977, p. 219. | MR | Zbl
and ,[23] Analyse harmonique et analyse pseudo-différentielle du cône de lumière, Astérisque, Vol. 156, Soc. Math. de France, Paris, 1987. | Numdam | MR | Zbl
,[24] C. R. Acad. Sci. Paris, T. 305, Series I, 1987, p. 415; T. 306, Series I, 1988, p. 111; T. 308, Series I, 1989, p. 397; Quantification relativiste, Mém. Soc. Math. France, n° 44/45, 1990. | MR
,[25] Differential Geometry, Lie Groups, and Symmetric Spaces, Academic, New York, 1978. | MR | Zbl
,[26] Commun. Math. Phys., Vol. 55, 1977, p. 1. | Zbl
,[27] Acta Math., Vol. 136, 1976, p. 1. | MR | Zbl
and ,[28] Ann. Math., Vol. 111, 1980, p. 253. | MR | Zbl
,[29] J. Funct. Anal., Vol. 81, 1988, p. 126. | MR | Zbl
and ,[30]
, private communication.[31] Ann. Inst. H. Poincaré, Phys. Théor., Vol. 54, 1991, p. 245. | Numdam | MR | Zbl
,[32] J. Math. Phys., Vol. 32, 1991, p. 1609. | MR | Zbl
and ,[33] Relativistic quantum frames (in preparation). | Zbl
, and ,[34] Squeezed coherent states (in preparation).
, and ,[35] Quantization, Coherent States and Diffeomorphism Groups, in Differential Geometry, Group Representations and Quantization, J. HENNIG, W. LÜCKE and J. TOLAR Eds., Lect. Notes Phys. , Vol. 379, Springer-Verlag, Berlin, 1991, p. 147. | MR
and ,[36] Poincaré coherent states: the two-dimensional massless case, Preprint UCL-IPT-91-12. | MR
and ,[37] Phys. Rev., Vol. D 18, 1978, p. 3655. | MR
,[38] J. Math. Phys., Vol. 27, 1986, p. 2936. | MR | Zbl
and ,[39] The Physics of Phase Space, Proc. Maryland, 1986, p. 330; Y. S. KIM and W. W. ZACHARY Eds., Lect. Notes Phys., Vol. 278, Springer, Berlin, 1987. | MR
and , in[40] Phys. Rev., Vol. A 41, 1990, p. 1199. | MR
and ,[41] Group Theoretical Methods in Physics (Proc. Ste Adèle, 1988, p. 380; Y. SAINT-AUBAIN and L. VINET Eds., World Scientific, Singapore, 1989. | MR
and , in