Runge-Lenz Vector as a 3d Projection of SO(4) Moment Map in $\mathbb{R}^{4}\times\mathbb{R}^{4}$ Phase Space
Classical Physics
2023-06-02 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
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, RL vector is a consequence of geometric symmetry of phase space.
Cite
@article{arxiv.2212.04931,
title = {Runge-Lenz Vector as a 3d Projection of SO(4) Moment Map in $\mathbb{R}^{4}\times\mathbb{R}^{4}$ Phase Space},
author = {Hitoshi Ikemori and Shinsaku Kitakado and Yoshimitsu Matsui and Toshiro Sato},
journal= {arXiv preprint arXiv:2212.04931},
year = {2023}
}
Comments
Corrected typographical error. The final version is published in J. Phys. A