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.
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     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},
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     number = {4},
     year = {1991},
     mrnumber = {1144105},
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     url = {http://www.numdam.org/item/AIHPA_1991__55_4_857_0/}
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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://www.numdam.org/item/AIHPA_1991__55_4_857_0/

[1] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, 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

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

[3] J.R. Klauder and B.S. Skagerstam, Coherent States. Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985. | MR | Zbl

[4] S. Debièvre, J. Math. Phys., Vol. 30, 1989, p. 1401.

[5] R.J. Duffin and A.C. Schaeffer, Trans. Am. Math. Soc., Vol. 72, 1952, p. 341. | MR | Zbl

[6] I. Daubechies, A. Grossmann and Y. Meyer, J: Math. Phys., Vol. 27, 1986, p. 1271. | MR | Zbl

[7] S.T. Ali and J.-P. Antoine, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 51, 1989, p. 23. | Numdam | MR | Zbl

[8] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 52, 1990, p. 83. | Numdam | MR | Zbl

[9] V.S. Varadarajan, Geometry of Quantum Theory. Vol. II. Quantum Theory of Covariant Systems, Van Nostrand Rheinhold, New York, 1970. | MR | Zbl

[10] J. Harnad, S. Shnider and L. Vinet, J. Math. Phys., Vol. 21, 1980, p. 2719. | MR | Zbl

[11] G.W. Mackey, Proc. Nat. Acad. Sci. (U.S.A.), Vol. 35, 1949, p. 537. | MR | Zbl

[12] J. Dixmier, Les C*-algèbres et leurs représentations, 2e éd., Gauthier-Villars, Paris, 1969. | MR | Zbl

[13] A. Grossmann, J. Morlet and T. Paul, J. Math. Phys., Vol. 26, 1985, p. 2473. | MR | Zbl

[14] S.T. Ali and N. Giovannini, Helv. Phys. Acta, Vol. 56, 1983, p. 1140.

[15] N. Giovannini, J. Math. Phys., Vol. 22, 1981, p. 2389. | MR

[16] N. Giovannini, Lett. Math. Phys., Vol. 5, 1981, p. 161. | MR | Zbl

[17] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 19. | MR | Zbl

[18] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 47. | Zbl

[19] B. Torrésani, 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] E. Prugovecki, J. Math. Phys., Vol. 19, 1978, p. 2260.

[21] G. Kaiser, J. Math. Phys., Vol. 18, 1977, p. 952; Vol. 19, 1978, p. 502.

[22] S.T. Ali and E. Prugovecki, J. Math. Phys., Vol. 18, 1977, p. 219. | MR | Zbl

[23] A. Unterberger, Analyse harmonique et analyse pseudo-différentielle du cône de lumière, Astérisque, Vol. 156, Soc. Math. de France, Paris, 1987. | Numdam | MR | Zbl

[24] A. Unterberger, 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] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic, New York, 1978. | MR | Zbl

[26] G. Mack, Commun. Math. Phys., Vol. 55, 1977, p. 1. | Zbl

[27] H. Rossi and M. Vergne, Acta Math., Vol. 136, 1976, p. 1. | MR | Zbl

[28] M. Flensted-Jensen, Ann. Math., Vol. 111, 1980, p. 253. | MR | Zbl

[29] G. Olafsson and B. Ørsted, J. Funct. Anal., Vol. 81, 1988, p. 126. | MR | Zbl

[30] S. Debièvre, private communication.

[31] G. Bohnké, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 54, 1991, p. 245. | Numdam | MR | Zbl

[32] J.R. Klauder and R.F. Streater, J. Math. Phys., Vol. 32, 1991, p. 1609. | MR | Zbl

[33] S.T. Ali, J.-P. Antoine and J.-P. Gazeau, Relativistic quantum frames (in preparation). | Zbl

[34] S.T. Ali, J.A. Brooke and J.-P. Gazeau, Squeezed coherent states (in preparation).

[35] S.T. Ali and G.A. Goldin, 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

[36] J.-P. Antoine and U. Moschella, Poincaré coherent states: the two-dimensional massless case, Preprint UCL-IPT-91-12. | MR

[37] E. Prugovecki, Phys. Rev., Vol. D 18, 1978, p. 3655. | MR

[38] S.T. Ali and G.G. Emch, J. Math. Phys., Vol. 27, 1986, p. 2936. | MR | Zbl

[39] S.T. Ali and H.-D. Doebner, in 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

[40] S.T. Ali and H.-D. Doebner, Phys. Rev., Vol. A 41, 1990, p. 1199. | MR

[41] J. Bertrand and P. Bertrand, in Group Theoretical Methods in Physics (Proc. Ste Adèle, 1988, p. 380; Y. SAINT-AUBAIN and L. VINET Eds., World Scientific, Singapore, 1989. | MR