Coherent states of the 1+1 dimensional Poincaré group : square integrability and a relativistic Weyl transform
Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 1, pp. 23-44.
@article{AIHPA_1989__51_1_23_0,
     author = {Ali, S. Twareque and Antoine, J.-P.},
     title = {Coherent states of the 1+1 dimensional Poincar\'e group : square integrability and a relativistic Weyl transform},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {23--44},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {1},
     year = {1989},
     zbl = {0702.22024},
     mrnumber = {1029848},
     language = {en},
     url = {archive.numdam.org/item/AIHPA_1989__51_1_23_0/}
}
Ali, S. Twareque; Antoine, J.-P. Coherent states of the 1+1 dimensional Poincaré group : square integrability and a relativistic Weyl transform. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 1, pp. 23-44. http://archive.numdam.org/item/AIHPA_1989__51_1_23_0/

[1] J.R. Klauder and B.S. Skagerstam, Coherent States - Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985. | MR 826247 | Zbl 1050.81558

[2] A. Perelomov, Generalized Coherent States and Their Applications, Springer, Berlin, 1986. | MR 899736 | Zbl 0605.22013

[3] J. Dixmier, Les C*-algèbres et leurs représentations, 2e éd., Gauthier-Villars, Paris, 1969. | MR 246136 | Zbl 0174.18601

[4] S.A. Gaal, Linear Analysis and Representation Theory, Springer, Berlin, 1973. | MR 447465 | Zbl 0275.43008

[5] M. Duflo and C.C. Moore, J. Funct. Anal., Vol. 21, 1976, p. 209. | Zbl 0317.43013

[6] A. Carey, Bull. Austral. Math. Soc., 15, 1976, p. 1; Rep. Math. Phys., Vol. 14, 1978, p. 247. | MR 430146 | Zbl 0418.22004

[7] A. Grossmann, J. Morlet and T. Paul, J. Math. Phys., Vol. 26, 1985, p. 2473; Ann. Inst. H. Poincaré, Vol. 45, 1986, p. 293. | Zbl 0571.22021

[8] M. Flensted-Jensen, Ann. of Math., Vol. 111, 1980, p. 253. | MR 569073 | Zbl 0462.22006

[9] H. Schlichtkrull, Invent. Math., Vol. 68, 1982, p. 497. | MR 669427 | Zbl 0501.22019

[10] S.T. Ali, Rivista del Nuovo Cim., Vol. 8, # 11, 1985, p. 1. | MR 821194

[11] E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime, D. Reidel, Dordrecht, 1984. | MR 741681 | Zbl 0536.60100

[12] S.T. Ali and H.D. Doebner, Quantization, topology and ordering, in Lect. Notes in Physics, Vol. 278, Springer, Berlin, 1987. | MR 915802

[13] A. Grossmann, G. Loupias and E.M. Stein, Ann. Inst. Fourier, Grenoble, Vol. 18, 1968, p. 343. | Numdam | MR 267425 | Zbl 0176.45102

[14] I. Daubechies and A. Grossmann, J. Math. Phys., Vol. 21, 1980, p. 2080. | MR 579204

[15] I. Daubechies, A. Grossmann and J. Reignier, J. Math. Phys., Vol. 24, 1983, p. 239. | MR 692298

[16] J.C.T. Pool, J. Math. Phys., Vol. 7, 1966, p. 66. | Zbl 0139.45903

[17] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 1. | MR 837718 | Zbl 0603.22010

[18] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 19. | Zbl 0603.22011

[19] S.T. Ali and E. Prugovecki, Acta Appl. Math., Vol. 6, 1986, p. 47. | Zbl 0603.22012

[20] R. Kunze, Pacific J. Math., Vol. 53, 1974, p. 465. | MR 374330 | Zbl 0321.22012

[21] A. Borel, Représentations des Groupes Localement Compacts; Lect. Notes in Mathematics, Vol. 276, Springer, Berlin, 1972. | Zbl 0242.22007

[22] H. Moscovici, Commun. Math. Phys., Vol. 54, 1977, p. 63. | MR 442152 | Zbl 0407.22011

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

[24] H. Moscovici and A. Verona, Ann. Inst. H. Poincaré, Vol. 29, 1978, p. 139. | Numdam | MR 513686 | Zbl 0392.22008

[25] H. Scutaru, Lett. Math. Phys., 2, 1977, p. 101. | MR 507248 | Zbl 0395.22009

[26] A.M. Perelomov, Commun. Math. Phys., Vol. 26, 1972, p. 222 (reprinted in Ref. 1); ibid., Vol. 44, 1975, p. 197. | MR 363209 | Zbl 0243.22016

[27] I.M. Gel'Fand and N. Ya. Vilenkin, Generalized Functions, Vol. 4, Academic Press, New York, 1964.

[28] J.-P. Antoine, J. Math. Phys., Vol. 10, 1969, pp. 53, 2276. | Zbl 0172.56602

[29] E. Nelson, Annals of Math., Vol. 70, 1959, p. 570. | MR 107176

[30] P. Bona, Czech. J. Phys., Vol. B33, 1983, p. 837.

[31] S.T. Ali and S. De Bièvre, in XYIth International Colloquium on Group-Theoretical Methods in Physics (Proceedings, Varna, 1987); Lecture Notes in Physics, Vol. 313, p. 201; H.-D. DOEBNER, J.-D. HENNIG, T. D. PALEV Eds., Springer, Berlin, 1988. | Zbl 0675.22010

[32] S. De Bièvre, J. Math. Phys., vol. 30, 1989, p. 1401. Toronto, 1988 (preprint). | MR 1002242 | Zbl 0686.46049