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Framing Noether’s Theorem

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Document pages: 13 pages

Abstract: We discuss Noether’s theorem from a new perspective and show that the spatialcontinuous symmetries of a system are on one hand symmetries of thespace and on the other hand are dictated by the system’s potential energy. TheNoether’s charges arising from an infinitesimal motion, or a Killing vectorfield, of the space, are conserved if the Lie derivative of the potential energy bythis vector field vanishes. The possible spatial symmetries of a mechanicalsystem are listed according to the potential energy of the external forces.

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