Volume 12, Issue 2, May 2005, Pages 230 - 252
Separable Potentials and a Triality in Two-Dimensional Spaces of Constant Curvature
José F. CARINENA, Manuel F RAÑADA, Mariano SANTANDER
José F. CARINENA
Received 1 December 2004, Accepted 1 February 2005, Available Online 1 May 2005.
- https://doi.org/10.2991/jnmp.2005.12.2.6How to use a DOI?
- We characterize and completely describe some types of separable potentials in twdimensional spaces, S2 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 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 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 2 .
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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 -