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

AI Thread Summary
Noether's theorem states that every continuous symmetry of a Lagrangian corresponds to a conserved quantity. The discussion highlights confusion regarding the precise interpretation and presentation of the theorem in literature. A participant emphasizes the importance of including time in discussions of symmetries, even when using simplified analogies. The conversation suggests that a more elementary treatment of the theorem could clarify its implications. Overall, the precise heuristic argument revolves around the relationship between symmetries and conservation laws in physics.
liorde
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Hi,
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?
precise argument is that any continuous symmetry of lagrangian i.e. which can be build up from infinitesimal ones implies a conserved quantity.Also you have forgotten the action in your two dimensional case i.e. where is time?
 
I excluded time because I used a 2D space analogy, which was easy to illustrate in a figure. I'm interested in the idea, so it doesn't matter if I use time or not.
 
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