# Conservation of Weak Charge?

1. Jan 16, 2009

### Phrak

Charge is conserved in particle interactions. Color is conserved. Inerial mass is conserved locally. Is weak hypercharge conserved?

2. Jan 16, 2009

### malawi_glenn

3. Jan 16, 2009

### Sideways

Yes it is.

The wikipedia article is pretty good if you want to learn more.

(By the way, Jefferson Laboratory in Newport News, Virginia is soon starting a major experiment to measure the weak charge of the proton.)

According to electroweak unification theory (part of the Standard Model), weak hypercharge ties directly into the electromagnetic properties of particles.

4. Jan 16, 2009

### humanino

I thought Jefferson Lab was a place were people study the strong interaction. Why did they decide to measure the weak charge ? Because they can ? Can they ? How difficult will this be ?

5. Jan 16, 2009

### Sideways

JLab was originally made strictly as an electromagnetic probe of nucleons and nuclei, but their mission has expanded a bit. It's a very tricky experiment; it will take something like a year of running time in one of the 3 research halls, if I recall correctly.

Layman's description of the experiment:

http://www.jlab.org/qweak/

6. Jan 16, 2009

### humanino

Your statement is very misleading. It will take the entire tentatively scheduled beam time of JLab's Hall C for 3 years. Some people must have considered they had to deeply update JLab's mission. I'm not sure to get the point when I see the projected plot

7. Jan 17, 2009

### Phrak

I didn't see anything in the Wikipedia article motivating weak charge conserveration. A little more searching, and I didn't find anything motivation conservation of electric charge within quatum field theory, either. I don't see the symmetry that would motivate either charge.

Why should electric, the weak charge, or their composite be conserved?

Last edited: Jan 17, 2009
8. Jan 17, 2009

### malawi_glenn

electric charge is conserved if you do the Noethers theorem. Same with weak charge.

9. Jan 17, 2009

Staff Emeritus
I'm afraid I am going to have to disagree with the majority (and Wikipedia). I don't see how weak hypercharge can possibly be conserved. The left-handed and right-handed electrons have different weak hypercharge. I can flip the spin with a magnetic interaction: $e_L + \gamma \rightarrow e_R + \gamma$, and now the left and right hand sides of the equation have different weak hypercharge.

Furthermore, if it were conserved, it's gauge field, the B, would be massless. It's not - it's not even in an eigenstate of mass.

Weak hypercharge is a broken symmetry. If the symmetry were unbroken, it would be conserved. But that's not the universe we live in.

10. Jan 17, 2009

### Phrak

Which symmetry and variation of Noether's theorem applies?

11. Jan 18, 2009

### malawi_glenn

Pick up any source on intro QED

12. Jan 18, 2009

### Phrak

Malawi! you're so inegmatic. Can I buy a clue? Where in Weinberg?

13. Jan 18, 2009

### malawi_glenn

Well if you can agree that Maxwells equations state conservation of electrc charge then QED should have that property. I don't have my Weinberg at home, but if you have peskin the argument is in ch3 "quantization of the Dirac field", see page 62.

14. Jan 18, 2009

### Phrak

Thanks for responing so quickly. Weinberg vol. I is all I have.

But that's interesting. I get charge convervation in Maxwell via other means than Noether. It results from the Maxwell tensor being antisymmetric. $$F_{\mu\nu}=F_{[\mu\nu]} I can't identify the argument in Weinberg, volume I. 15. Jan 18, 2009 ### malawi_glenn oh let me see if I can help you with that, since you have that the Maxwell tensor (aka electromagnetic field tensor) is antisymmetric, we have [tex] \partial _\nu F^{\mu \nu} = 0$$ so that we get the equation of continuity for electric charge. But another way to see this is by considering the action $$S = \int F^{\mu \nu}F_{\mu \nu} d^4x$$ and using noethers theorem on that one and euler lagrange equation of motion.

Weinberg is perhaps not the best place to start QFT... Mandl or Peskin is probably better introductory books.

Now I am not an expert on the electroweak theory (yet) but I have to say now that Vanadium seems to be entirely correct and that wiki article should be edited/motivated

16. Jan 18, 2009

### Phrak

Wonderful! That's what I needed to get started, I'm sure. You know, this is all Vanadium's fault in the first place. He's the one who got me started on this.

17. Jan 18, 2009

### malawi_glenn

hahahaha yeah blaim him ;-) He is a real trouble maker :-D

18. Jan 19, 2009

### Phrak

malawi, thanks for all your help. I hope you keep this thread subscribed.

This is a very interesting issue for me. One the one hand, electric charge conservation is a direct result of simply imposing a 4-vector field on a (pseudo) Riemann manifold, of any Christoffel connection, and the definition of charge as the divergence of E--nothing more.

I don't know how far you've gone in the mathematical angle of differentiable manifolds, but charge conservation is summed-up in the statement, "All exact forms are closed."

On the other hand, the usual method of finding conservation laws is via Noether, as you know.

Are these two derivations the same or different?
It could be shocking and profound if they cannot be found equivalent.

I have to learn Noether.

Last edited: Jan 19, 2009
19. Jan 19, 2009

### malawi_glenn

No Noether is as far as I know something different, but iam not 100% sure.

I've only done differntial geometry in class of General Relativity and one class in advanced analytical mechanics.

20. Jan 22, 2009

### Phrak

It's hard to say for me at this early date. Either way it should be interesting.

With some preliminary reading of Noether, this will take some time. I see that the Lagrangian $$\ F_{\mu\nu}F^{\mu\nu}$$ doesn't allow for field divergence. There are other formulations that include it. It's doesn't appear to be covariant--if not, it's applicable to Minkowski space, but not to Riemann Manifolds in general--but Minkowski space is the space used in particle physics, anyway. There are all sorts of issues, I need to resolve (and some review, as well!). I'd like to eventually see how it generalized to the electroweak force.

You could drop this thread and I'll pick it up later, I hope. But if you're interested in electromagnetism where the antisymmetry of the electromagnetic field tensor implies charge conservation, you could read Sean Carroll's Lecture Notes on General Relativity, available online in pdf format. His notes won't tell you about the antisymmetry of F_{\mu\nu} implying charge conservation; but it will introduce you to the powerful notation of differential forms that does.