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Analytic representations based on SU(1,1) coherent states and their applications

C. Brif·A. Vourdas·A. Mann
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Abstract

We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disk based on the SU(1,1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A ``weak'' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index $k$ is smaller than one half. Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.

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C. Brif, A. Vourdas, A. Mann. 1996-07-26. Analytic representations based on SU(1,1) coherent states and their applications. https://doi.org/10.1088/0305-4470/29/18/017

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