A generalized Noether theorem for scaling symmetry

P.-M. Zhang 1,2, M. Elbistan 2,3, P.A. Horvathy 3, P. Kosiński 4

1 School of Physics and Astronomy, Sun Yat-sen University, Zhuhai, 519082, China

2 Institute of Modern Physics, Chinese Academy of Sciences, China

3 IDP - Institut Denis Poisson, Orléans University, UMR 7013, Tours, France

4 Department of Computer Science, University of Lódź, Poland


The recently discovered conserved quantity associated with Kepler rescaling is generalized by an extension of Noether’s theorem which involves the classical action integral as an additional term. For a free particle, the familiar Schrödinger dilations are recovered. A general pattern arises for homogeneous potentials. The associated conserved quantity allows us to derive the virial theorem. The relation to the Bargmann framework is explained and illustrated by exact plane gravitational waves.


Virial theorem
Published by

Springer - The European Physical Journal Plus