Runge-Lenz Vector as a 3d Projection of SO(4) Moment Map in $\mathbb{R}^{4}\times\mathbb{R}^{4}$ Phase Space

Hitoshi Ikemori; Shinsaku Kitakado; Yoshimitsu Matsui; Toshiro Sato

doi:10.1088/1751-8121/accee7

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arXiv · 2212.04931

Runge-Lenz Vector as a 3d Projection of SO(4) Moment Map in $\mathbb{R}^{4}\times\mathbb{R}^{4}$ Phase Space

Hitoshi Ikemori·Shinsaku Kitakado·Yoshimitsu Matsui·Toshiro Sato

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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 $\mathbb{R}^4\times \mathbb{R}^4$ phase space.

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Hitoshi Ikemori, Shinsaku Kitakado, Yoshimitsu Matsui, Toshiro Sato. 2022-12-09. Runge-Lenz Vector as a 3d Projection of SO(4) Moment Map in $\mathbb{R}^{4}\times\mathbb{R}^{4}$ Phase Space. https://doi.org/10.1088/1751-8121%2Faccee7

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