Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 23 min ago
PreprintCC BY-NC-ND 4.0arXiv

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

  • Hitoshi Ikemori
  • Shinsaku Kitakado
  • Yoshimitsu Matsui
  • Toshiyuki Okubo
  • Toshiro Sato
Open at sourcePDFDOICite

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 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.

Related

  1. Order Reduction of Exponential Runge--Kutta Methods: Fourth-Order Schemes for Non-Commuting Operators
    Thi Tam Dang, Pablo Alexei Gazca-Orozco, Trung Hau Hoang
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv
  2. Adaptive Diagonally Implicit Runge-Kutta Methods Devoid of Order Reduction for Semilinear ODEs
    Steven B. Roberts, Abhijit Biswas, David Shirokoff +1
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. Dynamical quasi-symmetry of the classical Kepler-Coulomb problem and the conservation of the Laplace-Runge-Lenz vector
    Radosław Szmytkowski
    arXivPreprintarXiv licenceFull textMathematical physicsGeneral physicsarXiv
  4. An unified approach for the (inverted) quantum harmonic oscillator and the Berry-Keating hamiltonian
    Fabio Bagarello, Emanuele Balistreri, Sergey Kuzhel
    arXivPreprintarXiv licenceFull textMathematical physicsQuantum physics & quantum informationarXiv
  5. Combinatorics of noncommutative harmonic oscillator determinant
    Masato Wakayama, Wadim Zudilin
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{ikemori2026rungelenz,
  title = {{5D Runge-Lenz Vector from Symplectic Reduction of 8D Harmonic Oscillator}},
  author = {Hitoshi Ikemori and Shinsaku Kitakado and Yoshimitsu Matsui and Toshiyuki Okubo and Toshiro Sato},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27750},
  eprint = {2610.27750},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27750},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - 5D Runge-Lenz Vector from Symplectic Reduction of 8D Harmonic Oscillator
AU  - Hitoshi Ikemori
AU  - Shinsaku Kitakado
AU  - Yoshimitsu Matsui
AU  - Toshiyuki Okubo
AU  - Toshiro Sato
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27750
UR  - https://arxiv.org/abs/2610.27750
AB  - 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 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.
ER  -