Journal of Nonlinear Mathematical Physics

Volume 12, Issue 2, May 2005, Pages 230 - 252

Separable Potentials and a Triality in Two-Dimensional Spaces of Constant Curvature

Authors
José F. CARINENA, Manuel F RAÑADA, Mariano SANTANDER
Corresponding Author
José F. CARINENA
Available Online 1 May 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.2.6How to use a DOI?
Abstract
We characterize and completely describe some types of separable potentials in twdimensional spaces, S2 [1]2 , of any (positive, zero or negative) constant curvature and either definite or indefinite signature type. The results are formulated in a way which applies at once for the two-dimensional sphere S2 , hyperbolic plane H2 , AntiDeSiter / DeSitter two-dimensional spaces AdS1+1 / dS1+1 as well as for their flat analogues E2 and M1+1 . This is achieved through an approach of Cayley-Klein type with two parameters, 1 and 2, to encompass all curvatures and signature types. We dicuss six coordinate systems allowing separation of the Hamilton-Jacobi equation for natural Hamiltonians in S2 [1]2 and relate them by a formal triality transformation, which seems to be a clue to introduce general "elliptic coordinates" for any CK space concisely. As an application we give, in any S2 [1]2 , the explicit expressions for the Fradkin tensor and for the Runge-Lenz vector, i.e., the constants of motion for the harmonic oscillator and Kepler potential on any S2 [1]2 .
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 2
Pages
230 - 252
Publication Date
2005/05
ISBN
91-974824-4-7
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.2.6How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - José F. CARINENA
AU  - Manuel F RAÑADA
AU  - Mariano SANTANDER
PY  - 2005
DA  - 2005/05
TI  - Separable Potentials and a Triality in Two-Dimensional Spaces of Constant Curvature
JO  - Journal of Nonlinear Mathematical Physics
SP  - 230
EP  - 252
VL  - 12
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.2.6
DO  - https://doi.org/10.2991/jnmp.2005.12.2.6
ID  - CARINENA2005
ER  -