On realizations of nonlinear Lie algebras by differential operators
High Energy Physics - Theory
2009-10-31 v2
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.
Keywords
Cite
@article{arxiv.hep-th/9803253,
title = {On realizations of nonlinear Lie algebras by differential operators},
author = {J. Beckers and Y. Brihaye and N. Debergh},
journal= {arXiv preprint arXiv:hep-th/9803253},
year = {2009}
}
Comments
21 pages, Latex; New examples added in Sect. 3