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arXiv · 2610.27750

5D Runge-Lenz Vector from Symplectic Reduction of 8D Harmonic Oscillator

Hitoshi Ikemori·Shinsaku Kitakado·Yoshimitsu Matsui·Toshiyuki Okubo·Toshiro Sato
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Abstract

We derive the Runge-Lenz vector of the five-dimensional Kepler problem from the eight-dimensional harmonic oscillator through symplectic reduction. By rewriting the moment maps of the harmonic oscillator in terms of five-dimensional gamma matrices and the $\mathfrak{su}(2)$ generators associated with the symplectic reduction, we identify the moment map expected to yield the Runge-Lenz vector. We then perform the reduction with respect to the SU(2) symmetry, derive the five-dimensional Kepler Hamiltonian, and show explicitly that the identified moment map reduces to the Runge-Lenz vector.

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Hitoshi Ikemori, Shinsaku Kitakado, Yoshimitsu Matsui, Toshiyuki Okubo, Toshiro Sato. 2026-10-20. 5D Runge-Lenz Vector from Symplectic Reduction of 8D Harmonic Oscillator. https://arxiv.org/abs/2610.27750

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