# Quanta of massive vector fields

1. Jan 8, 2008

### quantumfireball

Are the W+,W- and Z0 the field quanta of the massive charged vector fields?????????
ie Proca fields

2. Jan 8, 2008

### olgranpappy

They are massive and they are gauge fields (electroweak force). but the Z0 is not charged.

3. Jan 8, 2008

### blechman

"Proca" fields are massive, spin-1 bosons. These objects are not unique. W and Z bosons are examples of these things. So is the rho meson in hadron physics. They are each their own separate Proca field.

4. Jan 8, 2008

### quantumfireball

but hadrons are not fundamental
but thanks for clearing the doubt regarding w bosons

5. Jan 8, 2008

### blechman

what does "fundamental" have to do with anything???

6. Jan 8, 2008

### quantumfireball

yes but Z0 field can be written as a linear combination of W+ and W- fields
like in scalar fields right?????????????to get a real valued field

7. Jan 8, 2008

### blechman

what I mean by my above post is that "Proca" has nothing to do with "fundamental" - it's just the Lagrangian for a massive, spin-1 particle. The deuteron, for example, can be described by a proca field, as long as you're not interested in the substructure of the deuteron (ex: problems in atomic or molecular physics)!

8. Jan 8, 2008

### blechman

NO!!!! The Z boson is NOT a linear combination of the charged W bosons! It is its own thing.

9. Jan 8, 2008

### olgranpappy

10. Jan 8, 2008

### quantumfireball

wait a minute this is getting a bit confusing in nucleur physics the pions are described by complex scalar fields and over there the neutral pion is decribed by the field 1/2*(phi+phi*),i think i read this in JJ Sakurai advanced QM
Plz confirm

11. Jan 8, 2008

### blechman

You are mis-informed! The neutral pion is not related to the charged pions - it is a linearly independent scalar field.

I think you're getting confused with the following: the 3 pions form an isospin-1 field (3 components), call them $\pi_1,\pi_2,\pi_3$. now you can write:

$$\pi^{\pm}=\frac{1}{\sqrt{2}}(\pi_1\pm i\pi_2)$$

while $\pi^0 = \pi_3$. Here the sign corresponds to the charge.

Now for the W bosons, you can also write $W^\pm\propto(W_1\pm iW_2)$ while the Z-boson is related to $W_3$, although the Z boson also has hypercharge so it's more complicated than the $\pi^0$.

Does that help?

12. Jan 8, 2008

### blechman

Also, in the quark model, remember that the charged pions are (u-dbar) and (d-ubar), while the neutral pion is (u-ubar)+(d-dbar) - so these are not the same thing!

13. Jan 8, 2008

### quantumfireball

thanks a lot belchman
i know i was a confused

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