Runge–Lenz vector as a 3d projection of SO(4) moment map in R4×R4 phase space

We show, using the methods of geometric algebra, that Runge–Lenz vector in the Kepler problem is a 3-dimensional projection of SO(4) moment map that acts on the phase space of 4-dimensional particle motion. Thus, Runge–Lenz vector is a consequence of geometric symmetry of R4×R4 phase space.