https://doi.org/10.1140/epjp/s13360-020-00247-5
Regular Article
A generalized Noether theorem for scaling symmetry
1
School of Physics and Astronomy, Sun Yat-sen University, Zhuhai, 519082, China
2
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China
3
Institut Denis Poisson, Tours University – Orléans University, UMR 7013, Tours, France
4
Department of Computer Science, Faculty of Physics and Applied Informatics, University of Lódź, Pomorska 149/153, 90-236, Lódź, Poland
* e-mail: mahmut.Elbistan@lmpt.univ-tours.fr
Received:
29
August
2019
Accepted:
24
January
2020
Published online:
5
February
2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
