Second order symmetries of the conformal laplacian and
R-separation

D 2015

Second order symmetries of the conformal laplacian and R-separation

MICHEL, Jean-Philippe; Fabian RADOUX a Josef ŠILHAN

Základní údaje

Originální název

Second order symmetries of the conformal laplacian and R-separation

Autoři

MICHEL, Jean-Philippe; Fabian RADOUX a Josef ŠILHAN

Vydání

BRISTOL, XXXTH INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (ICGTMP) (GROUP30), od s. 1-11, 11 s. 2015

Nakladatel

IOP PUBLISHING LTD

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10300 1.3 Physical sciences

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

URL

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/15:00116104

Organizační jednotka

Přírodovědecká fakulta

ISSN

Klíčová slova anglicky

HAMILTON-JACOBI EQUATIONS; VARIABLE-SEPARATION; KILLING TENSORS; SCHRODINGER-EQUATION; HELMHOLTZ EQUATIONS

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 31. 7. 2020 09:02, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Citovat

MICHEL, Jean-Philippe; Fabian RADOUX a Josef ŠILHAN. Second order symmetries of the conformal laplacian and R-separation. Online. In XXXTH INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (ICGTMP) (GROUP30). BRISTOL: IOP PUBLISHING LTD, 2015, s. 1-11. ISSN 1742-6588. Dostupné z: https://doi.org/10.1088/1742-6596/597/1/012058.

@inproceedings{1672338,
   author = {Michel, JeanandPhilippe and Radoux, Fabian and Šilhan, Josef},
   address = {BRISTOL},
   booktitle = {XXXTH INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (ICGTMP) (GROUP30)},
   doi = {https://doi.org/10.1088/1742-6596/597/1/012058},
   keywords = {HAMILTON-JACOBI EQUATIONS; VARIABLE-SEPARATION; KILLING TENSORS; SCHRODINGER-EQUATION; HELMHOLTZ EQUATIONS},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {BRISTOL},
   pages = {1-11},
   publisher = {IOP PUBLISHING LTD},
   title = {Second order symmetries of the conformal laplacian and R-separation},
   url = {https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012058},
   year = {2015}
}

TY  - CONF
ID  - 1672338
AU  - Michel, Jean-Philippe - Radoux, Fabian - Šilhan, Josef
PY  - 2015
TI  - Second order symmetries of the conformal laplacian and R-separation
PB  - IOP PUBLISHING LTD
CY  - BRISTOL
KW  - HAMILTON-JACOBI EQUATIONS
KW  - VARIABLE-SEPARATION
KW  - KILLING TENSORS
KW  - SCHRODINGER-EQUATION
KW  - HELMHOLTZ EQUATIONS
UR  - https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012058
L2  - https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012058
N2  - 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.
ER  -

MICHEL, Jean-Philippe; Fabian RADOUX a Josef ŠILHAN. Second order symmetries of the conformal laplacian and R-separation. Online. In \textit{XXXTH INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (ICGTMP) (GROUP30)}. BRISTOL: IOP PUBLISHING LTD, 2015, s.~1-11. ISSN~1742-6588. Dostupné z: https://doi.org/10.1088/1742-6596/597/1/012058.

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