This is a survey on the non-commutative harmonic oscillator, which is a generalization of usual (scalar) harmonic oscillators to the system introduced by Parmeggiani and Wakayama.With the definitions and the basic properties, we summarize the positivity of several related operators with sl2 interpretations. We also mention some unsolved questions, in order to clarify the current status of the problems and expected further development.
|Title of host publication||Symmetries, Integrable Systems and Representations|
|Publisher||Springer New York LLC|
|Number of pages||8|
|Publication status||Published - Jan 1 2013|
|Name||Springer Proceedings in Mathematics and Statistics|
All Science Journal Classification (ASJC) codes