Publication details
Second order symmetries of the conformal laplacian and R-separation
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Proceedings |
| Conference | XXXTH INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (ICGTMP) (GROUP30) |
| MU Faculty or unit | |
| Citation | |
| web | https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012058 |
| Doi | http://dx.doi.org/10.1088/1742-6596/597/1/012058 |
| Keywords | HAMILTON-JACOBI EQUATIONS; VARIABLE-SEPARATION; KILLING TENSORS; SCHRODINGER-EQUATION; HELMHOLTZ EQUATIONS |
| Description | Let (M, g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3, let Delta := del(a)g(ab)del(b) be the Laplace-Beltrami operator and let Delta(Y) be the conformal Laplacian. In some references, Kalnins and Miller provide an intrinsic characterization for R-separation of the Laplace equation Delta Psi = 0 in terms of second order conformal symmetries of Delta. The main goal of this paper is to generalize this result and to explain how the (resp. conformal) symmetries of Delta(Y) + V (where V is an arbitrary potential) can be used to characterize the R-separation of the Schrodinger equation (Delta(Y) + V)Psi = E Psi (resp. the Schrodinger equation at zero energy (Delta(Y) + V)Psi = 0). Using a result exposed in our previous paper, we obtain characterizations of the R-separation of the equations Delta(Y) Psi = 0 and Delta(Y) Psi = E Psi uniquely in terms of (conformal) Killing tensors pertaining to (conformal) Killing-Stackel algebras. |