Global Symmetries of the Kepler Problem

2021/04/28 by Joanna Gonera, Gonera, Joanna, Piotr Kosiński +3
Physics and Astronomy · #Classical Physics (physics.class-ph) #Exactly Solvable and Integrable Systems (nlin.SI) #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Orbital Angular Momentum in Optics #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.2104.14416

openalex publication_date 2021/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The global symmetry transformations generated by Runge-Lenz vector of twodimensional Kepler problem are explicitly described. They are given in terms of SU(2) left group multiplication with group elements being suitably parametrized by phase space points. The resulting non-linear action of SU(2) on the phase space is characterized in terms of the theory of nonlinear realizations developed in Phys. Rev. 177 (1969) 2239.

Citations

• On the Lie symmetries of the classical Kepler problem
• Structure of Phenomenological Lagrangians. I

Related

• On the Lie symmetries of the classical Kepler problem
• Revisiting Kepler: new symmetries of an old problem
• On Laplace-Runge-Lenz Vector as Symmetry Breaking order parameter in\n Kepler Orbit and Goldstone Boson
• Quantization of the Linearized Kepler Problem
• Generalisations of the Laplace-Runge-Lenz vector