Global Symmetries of the Kepler Problem

TL;DR

This paper explicitly describes the global symmetry transformations of the two-dimensional Kepler problem generated by the Runge-Lenz vector, using SU(2) group actions and nonlinear realization theory.

Contribution

It provides a detailed characterization of the SU(2) symmetry actions on phase space for the Kepler problem, linking them to nonlinear realization theory.

Findings

Explicit SU(2) symmetry transformations described

Nonlinear SU(2) action characterized on phase space

Connection to nonlinear realization theory established

Abstract

The global symmetry transformations generated by Runge-Lenz vector of twodimensional Kepler problem are explicitly described. They are given in terms of SU(2) left group multiplication with group elements being suitably parametrized by phase space points. The resulting non-linear action of SU(2) on the phase space is characterized in terms of the theory of nonlinear realizations developed in Phys. Rev. 177 (1969) 2239.