Electroweak Force and Unification

[Deified]

Can someone please explain to me why it is that we consider the electromagnetic and weak forces to be 'unified' but not the strong and electroweak? As far as I understand it (and I probably don't understand it very far at all) the electromagnetic and weak forces are the same thing at higher energies. I also understand that there is a 'unification energy' at which all the forces are one single force. So why the special status of 'unified' for the electroweak? Is it some relic of past, less complete understandings? Or (more likely) am I missing something?

 

Thanks for any light shed!

[insane_alien]

strong and electro-weak have been unified but its at far far far greater energies.

when we say unified we mean that we have observed the forces being unified so it has been proven.

[Severian]

Unfortunately the weak and electromagnetic interactions are not unified. I don't know who first used the word 'unified' for electroweak, but it seems to have spread like a cancer and now everyone says it. I often complain in talks when people say they are unified (though people look at me like I am a pedant).

 

To unify two forces together, as you say, they have to be manifestations of the same thing. So, for example electricity and magnetism are unified, since a Lorentz transformation maps one into the other (ie an electric field in one frame of reference is a magnetic field in another).

 

In QFT, in order to unify two forces, the coupling constants (a measure of how strong the force is) for the two forces have to become equal at some high energy. This is possible because the strengths change with energy, and (unless they are parallel) two lines will always meet at a point.

 

Usually above this unification scale there is a larger symmetry group. For example, it was hoped that the 3 forces could be unified by the symmetry group SU(5) and this symmetry would be broken down to U(1) (electromag) SU(2) (weak) and SU(3) (strong) at low energies since U(1), SU(2) and SU(3) are all subgroups of SU(5). This looks unlikely to work now, so we will probably need a bigger group, eg E6.

 

However, the 'electroweak theory' still still has two coupling constants (one for U(1) and one for SU(2)) so it is not unified. It just looks sort of unified because the two forces are mixed up.

[Royston]

However, the 'electroweak theory' still still has two coupling constants (one for U(1) and one for SU(2)) so it is not unified. It just looks sort of unified because the two forces are mixed up.

 

So even if the Higgs field is discovered to be correct, does that not change anything ?

 

EDIT: Forget I said that, I'm not thinking straight.

[Meir Achuz]

Unfortunately the weak and electromagnetic interactions are not unified. I don't know who first used the word 'unified' for electroweak' date=' but it seems to have spread like a cancer and now everyone says it. I often complain in talks when people say they are unified (though people look at me like I am a pedant).

 

To unify two forces together, as you say, they have to be manifestations of the same thing. So, for example electricity and magnetism are unified, since a Lorentz transformation maps one into the other (ie an electric field in one frame of reference is a magnetic field in another).

 

In QFT, in order to unify two forces, the coupling constants (a measure of how strong the force is) for the two forces have to become equal at some high energy. This is possible because the strengths change with energy, and (unless they are parallel) two lines will always meet at a point.

 

Usually above this unification scale there is a larger symmetry group. For example, it was hoped that the 3 forces could be unified by the symmetry group SU(5) and this symmetry would be broken down to U(1) (electromag) SU(2) (weak) and SU(3) (strong) at low energies since U(1), SU(2) and SU(3) are all subgroups of SU(5). This looks unlikely to work now, so we will probably need a bigger group, eg E6.

 

However, the 'electroweak theory' still still has two coupling constants (one for U(1) and one for SU(2)) so it is not unified. It just looks sort of unified because the two forces are mixed up.[/quote']

 

You do seem like a pedant.

The same alpha does appear in U(1) and SU(2).

That was the whole point.

Most low energy manifestations of the weak sector occur with the ratio

alpha/M_p^2, but it is the same alpha.

 

On the other hand, Strong and EW have only been "unified' in a theory

that is probably wrong, and at best incomplete.

[Severian]

You do seem like a pedant.

The same alpha does appear in U(1) and SU(2).

That was the whole point.

Most low energy manifestations of the weak sector occur with the ratio

alpha/M_p^2' date=' but it is the same alpha.

[/quote']

It is certainly not the same alpha. To specify the SM you still need two coupling parameters for the electroweak sector: [math]\alpha[/math] (the electromagnetic coupling) and [math]\sin^2 \theta_W[/math] (the Weinberg angle).

 

You can see this more explicitly from the group structure. The gauge bosons for each force are adjoint representations of the governing symmetry. An SU(N) symmetry has [math]N^2-1[/math] adjoints while a U(N) has N adjoints. So we have:

 

SU(3): [math]3^2-1=8[/math] gluons

SU(2): [math]2^2-1=3[/math], let's call them [math]W_1, W_2, W_3[/math]

SU(1): [math]1^2=1[/math], let's call it [math]B[/math]

 

When electroweak symmetry is broken, the [math]W_1[/math] and [math]W_2[/math] mix to give [math]W^\pm[/math] while the [math]W_3[/math] and [math]B[/math] mix to form the [math]Z[/math] boson and the photon.

 

This mixing to form the photon and the Z is the only place where the SU(2) and U(1) representations affect one another. Where is the loss of complexity you would expect from unification? Where did the other coupling go? In what sense could you possibly regard them as unified?

 

To put it another way, the two couplings before electroweak symmetry breaking are [math]g[/math] (SU(2)) and [math]g'[/math] (U(1)) which become [math]\alpha = \frac{e^2}{4\pi}[/math] and [math]\sin^2 \theta_W[/math] after breaking, where [math]\theta_W = \tan^{-1} \left(\frac{g'}{g} \right)[/math] and [math]e=g \sin \theta_W[/math].

[Meir Achuz]

g and g' look like 2 ccs, just like q_esu and q_emu.

That is before unification.

After unification, each case has one cc: alpha,

and a mixing parameter: v/c or theta_W.

Pedants argue over words.

[Severian]

So how is that unification? Where is the unification happening? Are you suggesting that they are not unified befoer symmetry breaking, but magically are unified after symmetry breaking?

[Deified]

This is all very interesting. Really. But just so I'm clear, all of the forces 'unify' (or whatever) at higher energies, in the same way that at higher energies the EM force and W force are the same. In other words, there's no particularly special connection between EM and W; we've just seen them 'unify' in the lab?

 

Sorry if I'm way off.

[J.C.MacSwell]

This is all very interesting. Really. But just so I'm clear' date=' [b']all of the forces 'unify' (or whatever) at higher energies[/b], in the same way that at higher energies the EM force and W force are the same. In other words, there's no particularly special connection between EM and W; we've just seen them 'unify' in the lab?

 

Sorry if I'm way off.

 

This is conjecture at this point. We have no idea of how or why. I thought the EM and W were the same at higher energies, not just connected, but I may have been mislead as Severian suggested. I thought Weinberg, Glashow and Salam won the Nobel prize for that?

[Meir Achuz]

The EM photon is a linear combination of the W_3 and B.

Yes. It is this particular breaking of the symmetry that unifies the U(1) and SU(2) groups. They can no longer be disjoint.

In a similar way, 100 years earlier, the E and B had to be in the same tensor, and could no longer be disjoint.

A similar unification has been conjectured for the SI with the EW, but that conjecture has not worked out yet, if ever.