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

Jean-Pierre Gazeau
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Jean-Pierre Gazeau: Université Paris 7 — Denis Diderot, LPTM

A chapter in Quantization, Coherent States, and Complex Structures, 1995, pp 147-158 from Springer

Abstract: 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.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1060-8_17

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DOI: 10.1007/978-1-4899-1060-8_17

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