TY - GEN
T1 - Non-commutative harmonic oscillators
AU - Ochiai, Hiroyuki
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84883416621&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84883416621&partnerID=8YFLogxK
U2 - 10.1007/978-1-4471-4863-0_19
DO - 10.1007/978-1-4471-4863-0_19
M3 - Conference contribution
AN - SCOPUS:84883416621
SN - 9781447148623
T3 - Springer Proceedings in Mathematics and Statistics
SP - 483
EP - 490
BT - Symmetries, Integrable Systems and Representations
PB - Springer New York LLC
ER -