TITLE:
Framing Noether’s Theorem
AUTHORS:
Caesar P. Viazminsky
KEYWORDS:
Noether’s Theorem, Continuous Spatial Symmetries, Conserved Momenta
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.3,
March
29,
2018
ABSTRACT:
We discuss Noether’s theorem from a new perspective and show that the spatial
continuous symmetries of a system are on one hand symmetries of the
space and on the other hand are dictated by the system’s potential energy. The
Noether’s charges arising from an infinitesimal motion, or a Killing vector
field, of the space, are conserved if the Lie derivative of the potential energy by
this vector field vanishes. The possible spatial symmetries of a mechanical
system are listed according to the potential energy of the external forces.