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I'm confused about the exact interpretation of Noether's theorem for fields. I find that the statement of the theorem and its proof are not presented in a precise manner in books.

My main question is: what is the precise heuristic argument that leads to Noether's theorem?

The question is presented in the attached pdf document.

Thanks

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# What is the Precise Heuristic Argument that Leads to Noether's Theorem

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