Physical origin of the Runge-Lenz vector

Jens Peder Dahl

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Abstract

The dynamical symmetry of the non-relativistic Kepler problem has attracted much attention in the scientific literature. In the present paper, we show that the Runge-Lenz vector, which accounts for the presence of this symmetry, has its physical origin in the generator of Lorentz transformations for the relativistic two-body problem. We reach this conclusion by considering the relativistic two-body problem, for the electromagnetic as well as for the gravitational interaction, in the 1/c2 approximation.
Original languageEnglish
JournalJournal of Physics A: Mathematical and General
Volume30
Issue number19
Pages (from-to)6831-6840
ISSN0305-4470
Publication statusPublished - 1997

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