Classical and quantum Kummer shape algebras
Mathematical Physics
2016-06-22 v1 math.MP
Abstract
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, is also presented.
Cite
@article{arxiv.1512.09279,
title = {Classical and quantum Kummer shape algebras},
author = {A. Odzijewicz and E. Wawreniuk},
journal= {arXiv preprint arXiv:1512.09279},
year = {2016}
}
Comments
39 pages, 2 figures