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

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 R 4 × R 4 phase space.

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Veröffentlicht in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2023-06, Vol.56 (22), p.225204
Hauptverfasser: Ikemori, Hitoshi, Kitakado, Shinsaku, Matsui, Yoshimitsu, Sato, Toshiro
Format: Artikel
Sprache:eng
Schlagworte:
Kepler system
Kustaanheimo–Stiefel transformation
moment map
Runge–Lenz vector
symplectic geometry
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Zusammenfassung: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 R 4 × R 4 phase space.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/accee7