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

被引：1

作者：

Ikemori, Hitoshi ^{[1
]}

Kitakado, Shinsaku ^{[2
]}

Matsui, Yoshimitsu ^{[3
]}

Sato, Toshiro ^{[4
]}

机构：

[1] Aichi Univ, Fac Econ, Nagoya, Aichi 4538777, Japan

[2] Nagoya Univ, Nagoya, Aichi 4648601, Japan

[3] Aichi Univ, Fac Law, Nagoya, Aichi 4538777, Japan

[4] Chukyo Univ, Sch Engn, Nagoya, Aichi 4668666, Japan

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2023年 / 56卷 / 22期

关键词：

symplectic geometry; moment map; Runge-Lenz vector; Kustaanheimo-Stiefel transformation; Kepler system; PREHISTORY;

D O I：

10.1088/1751-8121/accee7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 x R-4 phase space.

引用

页数：17

共 50 条

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