Geodesic Flow on an hyperboild model and the two-body motion under repulsive Coulomb forces

MESON, ALEJANDRO M.; VERICAT FERNANDO

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: [New York]; Año: 1998 vol. 39 p. 1993 - 1996

0022-2488

We show that in n dimension! the flow defined by the Hamiltonian system for two charged particles of the same sign, is mapped into the geodesic flow over the non-Euclidean space: Hn1t Hn22$P ¯ %, say the hyperboloid with the axis along e? 0 which besides having its ??boundaries at infinite?? identified, it is also punctured at the point P ¯ [(j 0 ,j 1 ,...,jn)5(21,0,...,0) ~corresponding to the collision states! and whose metric is of negative curvaturein n dimension! the flow defined by the Hamiltonian system for two charged particles of the same sign, is mapped into the geodesic flow over the non-Euclidean space: Hn1t Hn22$P ¯ %, say the hyperboloid with the axis along e? 0 which besides having its ??boundaries at infinite?? identified, it is also punctured at the point P ¯ [(j 0 ,j 1 ,...,jn)5(21,0,...,0) ~corresponding to the collision states! and whose metric is of negative curvature