Family of N-dimensional superintegrable systems and quadratic algebra structures

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2016). Family of N-dimensional superintegrable systems and quadratic algebra structures. In: C. Burdik, O. Navratil and S. Posta, XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23). 23rd International Conference on Integrable Systems and Quantum Symmetries, ISQS 2015, Prague, Czech Republic, (). 23 - 27 June 2015. doi:10.1088/1742-6596/670/1/012024


Author Hoque, Md Fazlul
Marquette, Ian
Zhang, Yao-Zhong
Title of paper Family of N-dimensional superintegrable systems and quadratic algebra structures
Formatted title
Family of N-dimensional superintegrable systems and quadratic algebra structures
Conference name 23rd International Conference on Integrable Systems and Quantum Symmetries, ISQS 2015
Conference location Prague, Czech Republic
Conference dates 23 - 27 June 2015
Proceedings title XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23)   Check publisher's open access policy
Journal name Journal of Physics: Conference Series   Check publisher's open access policy
Place of Publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Publication Year 2016
Sub-type Fully published paper
DOI 10.1088/1742-6596/670/1/012024
Open Access Status DOI
ISSN 1742-6596
1742-6588
Editor C. Burdik
O. Navratil
S. Posta
Volume 670
Issue 1
Total pages 7
Collection year 2017
Language eng
Formatted Abstract/Summary
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in pure and applied mathematics. We overview two new families of superintegrable Kepler-Coulomb systems with non-central terms and superintegrable Hamiltonians with double singular oscillators of type (n, N - n) in N-dimensional Euclidean space. We present their quadratic and polynomial algebras involving Casimir operators of so(N + 1) Lie algebras that exhibit very interesting decompositions Q(3) ⊕ so(N - 1), Q(3) ⊕ so(n) ⊕ so(N - n) and the cubic Casimir operators. The realization of these algebras in terms of deformed oscillator enables the determination of a finite dimensional unitary representation. We present algebraic derivations of the degenerate energy spectra of these systems and relate them with the physical spectra obtained from the separation of variables.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Conference Paper
Collections: School of Mathematics and Physics
HERDC Pre-Audit
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 0 times in Thomson Reuters Web of Science Article
Scopus Citation Count Cited 0 times in Scopus Article
Google Scholar Search Google Scholar
Created: Tue, 26 Apr 2016, 01:46:13 EST by System User on behalf of Learning and Research Services (UQ Library)