6 Hidden \(\mathfrak {so}(4)\) Symmetry

The previous chapter showed that the bracket of the Lenz observables contains the factor \(-2mH\). So the symmetry algebra depends on the sign of the energy. For bounded Kepler motion we only need the negative-energy case. In that case, after restricting to a fixed-energy surface and rescaling the Lenz vector, the conserved quantities \(L\) and \(A\) combine into an \(\mathfrak {so}(4)\) symmetry.