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Analytic Representations Based on SU(1,1) Lie Algebra Coherent States for Squeezed Displaced Fock States

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Abstract

The coherent states (CSs) of the SU(1,1) group can be divided into two broad categories: (a) the Barut-Girardello coherent states (BGCSs) and (b) the Perelomov coherent states (PCSs). Some definitions for the squeezed displaced Fock states (SDFSs) are given. The hyperbolic analytic representation in the complex plane is considered. An analytic representation of the SU(1,1) Lie group is given and the representation in the unit disk based on the SU(1,1) PCSs for SDFSs is considered.

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References

  1. Weyl, H.: Z. Phys. 46, 1 (1927)

    Article  Google Scholar 

  2. Weyl, H.: The Theory of Groups and Quantum Mechanics. New York, Dover (1950)

    Google Scholar 

  3. Wünsche, A.: J. Opt., B. Quantum Semiclass. Optics 2, 73 (2000)

    Article  Google Scholar 

  4. Perelomov, A.M.: Generalized Coherent States and their Applications. Springer, Berlin Heidelberg New York (1986)

    MATH  Google Scholar 

  5. Král, P.: J. Modern Opt. 37, 889 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Král, P.: Phys. Rev. A. 42, 4177 (1990)

    Article  MathSciNet  Google Scholar 

  7. Obada, A.-S.F., Abd Al-Kader, G.M.: J. Modern Opt. 45, 713 (1998)

    Google Scholar 

  8. Obada, A.-S.F., Abd Al-Kader, G.M.: J. Modern Opt. 46, 263 (1999)

    Google Scholar 

  9. Stoler, D.: Phys. Rev. D. 1, 3217 (1970)

    Article  Google Scholar 

  10. Stoler, D.: Phys. Rev. D. 4, 1925 (1971)

    Article  Google Scholar 

  11. Yuen, H.P.: Phys. Rev. A. 13, 2226 (1976)

    Article  Google Scholar 

  12. Loudon, R., Knight, P.L.: J. Modern Opt. 34, 709 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Glauber, R.J.: Phys. Rev. 131, 2766 (1963)

    Article  MathSciNet  Google Scholar 

  14. Brif, C., Vourdas, A., Mann, A.: J. Phys. A: Math. Gen. 29, 5873 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  15. Brif, C.: Internat. J. Theoret. Phys. 36, 1651 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Abd Al-Kader, G.M., Obada, A.-S.F.: Internat. J. Theoret. Phys., Group Theory, and Nonlinear Optics 8, 293–318 (2002)

  17. Abd Al-Kader, G.M., Obada, A.-S.F.: In: George, T.F., Arnoldus, H.F. (eds.) Theoretical Physics 2002, Part 2, pp. 35–59. Nova Science Publishers (2003)

  18. Abd Al-Kader, G.M., Obada, A.-S.F.: Internat J. Theoret Phys., Group Theory, and Nonlinear Optics 11(4), 1 (2006)

  19. Vourdas, A.: J. Phys. A: Math. Gen. 39, R65–R141 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  20. Barut, A.O., Girardello, L.: Comm. Math. Phys. 21, 41 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  21. Wang, X.-G.: Internat J. Modern Phys. B. 14, 1093 (2000)

    MathSciNet  Google Scholar 

  22. Marian, P.: Phys. Rev. A. 44, 3325 (1991)

    Article  Google Scholar 

  23. Marian, P.: Phys. Rev. A. 45, 2044 (1992)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt

    Gamal Mohamed Abd Al-Kader & Abdel-Shafy F. Obada

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  1. Gamal Mohamed Abd Al-Kader
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  2. Abdel-Shafy F. Obada
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Correspondence to Gamal Mohamed Abd Al-Kader.

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Abd Al-Kader, G.M., Obada, AS.F. Analytic Representations Based on SU(1,1) Lie Algebra Coherent States for Squeezed Displaced Fock States. Appl Categor Struct 16, 3–11 (2008). https://doi.org/10.1007/s10485-006-9032-9

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  • DOI: https://doi.org/10.1007/s10485-006-9032-9

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