January 27th, 2021

“Kepler Harmonies” and conformal symmetries

Пишут, будто пару лет назад открыли новый закон сохранения в классической механике (если я правильно понял), соответствующий третьему закону Кеплера (!):

"The rescaling (I.2) is therefore not a symmetry for the Keplerian system in the above sense and therefore no Noetherian conserved quantity is expected to arise ; textbooks call it a “similarity” [1]. It came therefore as a surprise that the Kepler problem does have a conserved quantity associated with (I.2) – which is however of a nonconventional form, involving also the classical Hamiltonian action [2],
....
where the integration is along the classical trajectory in 3-space. This novel conserved quantity which seems to have escaped attention until recently was obtained in [2] in a remarkably indirect way : the Kepler problem was first “E-D” (Eisenhart Duval) lifted to a 5-dimensional “Bargmann” manifold
".

https://arxiv.org/pdf/1903.05070.pdf
https://www.sciencedirect.com/science/article/pii/S0370269319302266