Non-commutative harmonic oscillators

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


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
Number of pages8
ISBN (Print)9781447148623
Publication statusPublished - 2013

Publication series

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

All Science Journal Classification (ASJC) codes

  • General Mathematics


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