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

1. ### liorde

15
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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2. ### andrien

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?

3. ### liorde

15
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.