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

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
Attached Files
 q1.pdf (139.7 KB, 19 views)

 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.

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

if you are looking for some elementary treatment then this might help.I am not sure what is really the problem.
http://www.mathpages.com/home/kmath564/kmath564.htm