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

[liorde]

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

 

[andrien]

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?

 

[liorde]

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.

 

[andrien]

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