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Non-commutative Harmonic Oscillators

  • Hiroyuki Ochiai
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 40)

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 \(\mathfrak{sl}_{2}\) interpretations. We also mention some unsolved questions, in order to clarify the current status of the problems and expected further development.

Notes

Acknowledgements

This work is partially supported by JSPS Grant-in-Aid for Scientific Research (A) #19204011, and JST CREST.

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

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