In this answer, conservation of LRL vector (classical and quantum) $$ \vec A=\frac1{2m}(\vec p\times \vec L-\vec L\times \vec p)-\frac{q^2}{r}\hat r, $$ was related to $SO(4)$ symmetry, but no further explanation was given. Is it true? How can one prove it?
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In this doc, section D, $SO(4)$ structure is mentioned. It's not lorentz symmetry. – Luessiaw Feb 02 '23 at 07:22
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This paper is more clear. – Luessiaw Feb 02 '23 at 07:32
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2Possible duplicate: How to see the ${\rm SO}(4)$ symmetry of the classical Kepler problem? Related: How can one see that the Hydrogen atom has $SO(4)$ symmetry? – Qmechanic Feb 02 '23 at 07:40