Second order symmetries of the conformal laplacian and R-separation
(2015) 30th International Colloquium on Group Theoretical Methods in Physics (Group30), ICGTMP 2014 — Location: Ghent, Belgium (14.July.2014)
Files
No attached file found for this publication.
Details
- Authors
- Abstract
- Let (M, g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3, let Δ := ∇agab∇b be the Laplace-Beltrami operator and let ΔY be the conformal Laplacian. In some references, Kalnins and Miller provide an intrinsic characterization for R-separation of the Laplace equation ΔΨ = 0 in terms of second order conformal symmetries of Δ. The main goal of this paper is to generalize this result and to explain how the (resp. conformal) symmetries of ΔY + V (where V is an arbitrary potential) can be used to characterize the R-separation of the Schrodinger equation (ΔY + V)Ψ = EΨ (resp. The Schrodinger equation at zero energy (ΔY + V)Ψ = 0). Using a result exposed in our previous paper, we obtain characterizations of the R-separation of the equations ΔYΨ = 0 and ΔYΨ = EΨ uniquely in terms of (conformal) Killing tensors pertaining to (conformal) Killing-Stackel algebras.
- Affiliations
Citations
Michel, J.-P., Radoux, F., & Silhan, J. (2015). Second order symmetries of the conformal laplacian and R-separation. Journal of Physics: Conference Series, 597(1), 12058. https://doi.org/10.1088/1742-6596/597/1/012058 (Original work published 2015)