# Noether's Theorem and SU(2)

1. May 11, 2015

### nigelscott

Is it possible to prove that weak isospin associated with SU(2) is conserved using Noether's theorem?

2. May 11, 2015

Staff Emeritus
Considering that weak isospin is not conserved, the answer is "no".

3. May 11, 2015

### nigelscott

Maybe I asked the question in the wrong way (or maybe not!). It is possible to use Noether's theorem to show that U(1) symmetry is associated with charge (weak hypercharge). So how do you demonstrate mathematically that SU(2) is associated with weak isospin?

4. May 11, 2015

Staff Emeritus
5. May 12, 2015

### nigelscott

Certainly not taken the wrong way. I have no background in particle physics. I am a retired electrical engineer with a decent background in QM. I am trying to learn this stuff from books and videos (notably Susskind's videos on the Standard Model). There are lot of gaps that I am trying to fill and more often than not I get things messed up. But that's OK as long I keep learning and don't waste too many people's time . That said, I think I now have a basic understanding of symmetries and group generators. I understand that weak hypercharge is the generator of U(1) and weak isospin is the generator of SU(2). According to Noether, rotational symmetries are associated with charge. I thought there may be a corresponding argument that associates SU(2) with weak isospin.

Re the W boson post. Yes, you are correct about this too. However, responses to this post and others have helped me enormously. In retrospect, I would draw the same conclusion that you did about my level of understanding.

6. May 12, 2015