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SL(2, ℝ)-Coherent States and Integrable Systems in Classical and Quantum Physics

In: Quantization, Coherent States, and Complex Structures

Author

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  • Jean-Pierre Gazeau

    (Université Paris 7 — Denis Diderot, LPTM)

Abstract

The group SL(2, ℝ) ≅ SU(1, 1) ≅ Sp(1, ℝ) appears in various domains of physics as being the raison d’être of the integrability of the considered system. We do not here pretend to give an exhaustive list of such systems. We just want to stress the simplifying role played by the complex structure and the related coherent states which naturally appear for some of them. We also intend to clarify the relation existing between those different physical models, their respective complex structures and between two different types of coherent states, namely the SU(1, 1) Perelomov coherent states and the SU(1, 1) Barut-Girardello ones.

Suggested Citation

  • Jean-Pierre Gazeau, 1995. "SL(2, ℝ)-Coherent States and Integrable Systems in Classical and Quantum Physics," Springer Books, in: J.-P. Antoine & S. Twareque Ali & W. Lisiecki & I. M. Mladenov & A. Odzijewicz (ed.), Quantization, Coherent States, and Complex Structures, pages 147-158, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1060-8_17
    DOI: 10.1007/978-1-4899-1060-8_17
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