On the complete symmetry group of the classical Kepler system

A rather strong concept of symmetry is introduced in classical mechanics, in the sense that some mechanical systems can be completely characterized by the symmetry laws they obey. Accordingly, a ‘‘complete symmetry group’’ realization in mechanics must be endowed with the following two features: (1) the group acts freely and transitively on the manifold of all allowed motions of the system; (2) the given equations of motion are the only ordinary differential equations that remain invariant under the specified action of the group. This program is applied successfully to the classical Kepler problem, since the complete symmetry group for this particular system is here obtained. The importance of this result for the quantum kinematic theory of the Kepler system is emphasized.

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