Reversing Noether's theorem

Question

Noether's theorem states: any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is this statement invertible? I mean, if a conservation law exists, this implies there is a differentiable symmetry in the action?

score 3 · Accepted Answer · answered Jul 04 '14 at 08:37

Emmy Noether proved both the theorem and its converse. Look for the book "The Noether Theorems" for a precise and discussed formulation of her statements, as well as a translation of the original paper. It seems there is a link to the pdf in the princeton math website (I don't know about copyright issues, however).

Reversing Noether's theorem

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