A generalized Noether theorem for scaling symmetry

P. -M. Zhang, M. Elbistan, P. A. Horvathy, P. Kosinski

Published 2019-03-12Version 1

The recently discovered conserved quantity associated with Kepler's rescaling [1] is recovered by proving a generalised Noether's theorem. Applied to a free particle we get a two-parameter family of generalized rescaling symmetries, all of whose associated charges reduce however to a single one, namely to the familiar Schr\"odinger-dilation-charge. For a harmonic oscillator we get pure position rescaling, and the associated conserved quantity allows us to derive the virial theorem.