On realizations of nonlinear Lie algebras by differential operators
arXiv:hep-th/9803253 · doi:10.1088/0305-4470/32/15/008
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.
21 pages, Latex; New examples added in Sect. 3