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arXiv · hep-th/9803253

On realizations of nonlinear Lie algebras by differential operators

J. Beckers·Y. Brihaye·N. Debergh
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Abstract

We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear, quadratic and cubic cases are explicitly visited but the method works for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are studied in the context of these ``nonlinear'' Lie algebras and some examples dealing with quantum optics are pointed out.

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J. Beckers, Y. Brihaye, N. Debergh. 1998-12-17. On realizations of nonlinear Lie algebras by differential operators. https://doi.org/10.1088/0305-4470%2F32%2F15%2F008

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