Non-commutative harmonic oscillators

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationSymmetries, Integrable Systems and Representations
PublisherSpringer New York LLC
Pages483-490
Number of pages8
ISBN (Print)9781447148623
DOIs
Publication statusPublished - Jan 1 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume40
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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  • Cite this

    Ochiai, H. (2013). Non-commutative harmonic oscillators. In Symmetries, Integrable Systems and Representations (pp. 483-490). (Springer Proceedings in Mathematics and Statistics; Vol. 40). Springer New York LLC. https://doi.org/10.1007/978-1-4471-4863-0_19