|
This article is cited in 2 scientific papers (total in 2 papers)
Toward Classification of 2nd Order Superintegrable Systems in 3-Dimensional Conformally Flat Spaces with Functionally Linearly Dependent Symmetry Operators
Bjorn K. Berntsona, Ernest G. Kalninsb, Willard Miller Jr.c a Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
b Department of Mathematics, University of Waikato, Hamilton, New Zealand
c School of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA
Abstract:
We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD) symmetry generators, with special emphasis on complex Euclidean space. The symmetries for these systems are linearly dependent only when the coefficients are allowed to depend on the spatial coordinates. The Calogero–Moser system with 3 bodies on a line and 2-parameter rational potential is the best known example of an FLD superintegrable system. We work out the structure theory for these FLD systems on 3D conformally flat space and show, for example, that they always admit a 1st order symmetry. A partial classification of FLD systems on complex 3D Euclidean space is given. This is part of a project to classify all 3D 2nd order superintegrable systems on conformally flat spaces.
Keywords:
superintegrable systems, Calogero 3 body system, functional linear dependence.
Received: April 7, 2020; in final form December 9, 2020; Published online December 16, 2020
Citation:
Bjorn K. Berntson, Ernest G. Kalnins, Willard Miller Jr., “Toward Classification of 2nd Order Superintegrable Systems in 3-Dimensional Conformally Flat Spaces with Functionally Linearly Dependent Symmetry Operators”, SIGMA, 16 (2020), 135, 33 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1672 https://www.mathnet.ru/eng/sigma/v16/p135
|
Statistics & downloads: |
Abstract page: | 46 | Full-text PDF : | 32 | References: | 9 |
|