Two-body problem on spaces of constant curvature: I.~Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 249-264
Voir la notice de l'article provenant de la source Math-Net.Ru
We consider the problem of two bodies with central interaction that propagate in a simply connected space with a constant curvature and an arbitrary dimension. We obtain the explicit expression for the quantum Hamiltonian via the radial differential operator and generators of the isometry group of a configuration space. We describe the reduced classical mechanical system determined on the homogeneous space of a Lie group in terms of orbits of the coadjoint representation of this group. We describe the reduced classical two-body problem.
@article{TMF_2000_124_2_a4,
author = {A. V. Shchepetilov},
title = {Two-body problem on spaces of constant curvature: {I.~Dependence} of the {Hamiltonian} on the symmetry group and the reduction of the classical system},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {249--264},
publisher = {mathdoc},
volume = {124},
number = {2},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a4/}
}
TY - JOUR AU - A. V. Shchepetilov TI - Two-body problem on spaces of constant curvature: I.~Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2000 SP - 249 EP - 264 VL - 124 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a4/ LA - ru ID - TMF_2000_124_2_a4 ER -
%0 Journal Article %A A. V. Shchepetilov %T Two-body problem on spaces of constant curvature: I.~Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system %J Teoretičeskaâ i matematičeskaâ fizika %D 2000 %P 249-264 %V 124 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a4/ %G ru %F TMF_2000_124_2_a4
A. V. Shchepetilov. Two-body problem on spaces of constant curvature: I.~Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 249-264. http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a4/