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Noether conservation theorems
Posted:
Oct 12, 2007 10:34 AM


Many texts give a simple form of Emmy Noether's conservation theorem: Each oneparameter group of symmetries of a Lagrangian system gives a conserved quantity of that system. It is a beautiful result and entirely clear  once you are shown the proof.
But Noether proved two more involved versions of the theorem: Any finite dimensional Lie gorup action that preserves a Lagrangian gives some kind of family of conserved quantities that I do not yet understand, and an infinitedimensional Lie group gives something more complicated that I do not yet understand.
Several sources claim that the difference between the finite and infinitedimensional versions says something important about the failure of momentumenergy conservation in General Relativity.
Can anyone explain what they mean, or point me to sources?
Actually, I don't see how either version can say anything definitive about failure of conservation, since each seems to give sufficient but NOT necessary conditions for conservation of a quantity.
I'd appreciate any advice I can get on this.
best, Colin



