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Topic: Noether conservation theorems
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Colin McLarty

Posts: 11
Registered: 3/3/06
Noether conservation theorems
Posted: Oct 12, 2007 10:34 AM
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Many texts give a simple form of Emmy Noether's conservation theorem:
Each one-parameter 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 infinite-dimensional Lie group gives something more
complicated that I do not yet understand.

Several sources claim that the difference between the finite- and
infinite-dimensional versions says something important about the
failure of momentum-energy 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




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