What Are Practical Applications of Noether's Theorem for Beginners?

[CassiopeiaA]

Hi

I need a little help in my homework. It is not a direct problem to be solved. Rather I am supposed to find an application of Noether's theorem. All the article or papers I have found are very difficult for me to understand. In fact, I still don't understand any application of Noether's theorem yet, even after spending hours. Can anyone please help me or give me some hints to where to look at or which direction I should look into?

 

[DrClaude]

All the article or papers I have found are very difficult for me to understand.

You have labeled this thread "A", meaning that you want answers at a graduate level. Is that correct?

Have you looked at Wikipedia?

And it would probably help if you defined what is meant by "application."

 

[vanhees71]

Noether's theorem is of concern to (nearly) all of physics. So you should specify the problem first. Are you familiar with the action principle and variational calculus (which I consider a prerequisite to understand Noether's theorem)? Then you should tell us, where precisely you have problems with the understanding (classical mechanics or field theory). Best is a concrete problem in terms of a Lagrangian or Hamiltonian.

 

[CassiopeiaA]

I know lagrangian and hamiltonian dynamics and I need a graduate level answer. I do not have any knowledge of field theory, but I can understand the four-vector notations (I did a course on special theory of relativity.)

 

[vanhees71]

But what do you need then? Is it about point-particle mechanics (relativistic or non-relativistic doesn't make much difference concerning Noether's theorem)? Do you have an example, where you have difficulties to understand a symmetry argument? If so, perhaps it's easiest to start with this example. To write down a full general proof of Noether's theorem is a bit lengthy for the forum, I fear.