On the construction of generalized su(1, 1) coherent states

Reports on Mathematical Physics

Volumn 68, Issue 1, 2011, Pages 23-35

  Berrada, K ^a,b   Baz, M El ^a   Hassouni, Y ^a  

^a FACULTÉ DES SCIENCES   (Morocco)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

Generalized su(1, 1) algebra; Mandel's parameter; Quantum entanglement; Quantum groups; SU(1, 1) coherent states

Indexed keywords

EID: 80053537089     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(11)60025-6     Document Type: Article

References (33)

1. Schrödinger E. Naturwissenschaften 1926, 14:664.
2. Glauber R. The quantum theory of optical coherence. Phys. Rev. 1963, 130:2529.
3. Glauber R. Coherent and incoherent states of radiation field. J. Phys. Rev. 1963, 131:2766.
4. Klauder J.R. Continuous representation theory. I. Postulates of continuous representation theory. J. Math. Phys. 1963, 4:1055.
5. Klauder J.R. Generalized relation between quantum and classical dynamics. J. Math. Phys. 1963, 4:1058.
6. Klauder J.R., Skagertan B.-S. Coherent States 1985, World Scientifique, Singapore.
7. Perelomov A.M. Generalized Coherent States and Their Applications 1986, Springer, Berlin.
8. Ali S.T., Antoine J.-P., Gazeau J.-P. Coherent States, Wavelets and Their Generalizations 2000, Springer, New York.
9. Perelomov A.M. Coherent states for arbitrary Lie group. Commun. Math. Phys. 1972, 26:222.
10. Gilmore R. Geometry of symmetrized states. Ann. Phys. (NY) 1972, 74:391.
11. Zhang W.-M., Feng D.H., Gilmore R. Coherent states: Theory and some applications. Rev. Mod. Phys. 1990, 26:867.
12. A. Inomata, H. Kuratsuji and C. C. Gerry: Path Integrals and Coherent States of SU(2) and SU(1,1), Singapore: World Scientific 1992.
13. Barut A.O., Girardello L. New coherent states associated with non compact groups. Commun. Math. Phys. 1971, 21:41.
14. Drinfeld V.G. Quantum Groups. Proc. of the 1986 Int. Congress of Math 1987, 798. AMS, Berkeley, 1986.
15. Jimbo M. A q-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys. 1985, 10:63.
16. El Baz M., Hassouni Y., Madouri F. New construction of coherent states for generalized harmonic oscillators. Rep. Math. Phys. 2002, 50:263.
17. Jurčco B. On coherent states for the simplest quantum groups. Lett. Math. Phys. 1991, 21:51.
18. Ellinas D. Path integrals for quantum algebras and the classical limit. J. Phys. A 1993, 26:L543.
19. q(2) and a q-analogue of the boson operators. J. Phys. 1989, A22:L873.
20. q(2). J. Phys. A 1989, 22:4581.
21. Arik M., Coon D.D. Hilbert spaces of analytic functions and generalized coherent states. J. Math. Phys. 1976, 17:524.
22. Perelomov A.M. On the completeness of some subsystems of q-deformed coherent states. Helv. Phys. Acta 1996, 68:554.
23. Chakrabarti R., Jagannathan R. A (p,q)-oscillator realization of two-parameter quantum algebras. J. Phys. 1991, A24:L711.
24. q(1, 1) algebra. J. Phys. A: Math. Gen. 2004, 37:10561.
25. El Baz et M., Hassouni Y. Special deformed exponential functions leading to more consistent Klauder's coherent states. Phys. Lett. A 2002, 300:361.
26. Klauder J.R., Penson K.A., Sixdeniers J.-M. Constructing coherent states through solutions of Stieltjes and Hausdorff moment problems. Phys. Rev. A 2001, 64:013817.
27. Gasper G., Rahman M. Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, 35 1990, Cambridge University Press, Cambridge.
28. Gazeau J.P., Champagne B. The Fibonacci-deformed harmonic oscillator. Algebraic Methods in Physics, CRM Series in Theoretical and Mathematical Physics 2000, vol 3. Springer, Berlin. Y. Saint-Aubin, L. Vinet (Eds.).
29. Mandel L., Wolf E. Optical Coherence and Quantum Optics 1995, Cambridge University Press, Cambridge.
30. Katriel J., Solomon A.I. Phys. Rev. A 1994, 49:5149.
31. Berrada K., El Baz M., Saif F., Hassouni Y., Mnia S. Entanglement generation from deformed spin coherent states using a beam splitter. J. Phys. A 2009, 42:285306.
32. Gerry C.C., Benmoussa A. Phys. Rev. A 2005, 71:062319.
33. Markham D., Vedral V. Phys. Rev. A 2005, 67:042113.