Explanation of terminology: electroweak

In summary, electroweak is a term used in particle physics to describe the unification of the electromagnetic and weak forces. It is a fundamental theory that explains the interactions between particles at the subatomic level. The electroweak theory was developed in the 1960s and has been extensively tested and confirmed through experiments. It plays a crucial role in understanding the behavior of particles and the workings of the universe.
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dextercioby
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I'm not a specialist in this subject, so bear with me. I've always wondered why one claims that the electromagnetic and weak interactions are unified, but the strong one with the (unified) other two is not.
Mathematically, I'm aware that the full gauge group of the SM is ## U(1) \times SU(2) \times SU(3) ##, so one perceives all three interactions separately and on equal footing. In what exact sense are the weak and the em unified, but the strong not?

Thank you!
 
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  • #2
Since this is an A, what do you think the U(1) and SU(2) are?
 
  • #3
dextercioby said:
I'm not a specialist in this subject, so bear with me. I've always wondered why one claims that the electromagnetic and weak interactions are unified, but the strong one with the (unified) other two is not.
Mathematically, I'm aware that the full gauge group of the SM is ## U(1) \times SU(2) \times SU(3) ##, so one perceives all three interactions separately and on equal footing. In what exact sense are the weak and the em unified, but the strong not?

Thank you!
To follow up on Vanadium's post:

U(1) has one generator and SU(2) has three generators. The key questions are: The E&M gauge field is associated to which of these generators? The ## Z_0## is associated to which ones? What about the ##W^\pm##?
 
  • #4
U(1) is the gauge group of electromagnetism, while SU(2)w is the gauge group of the weak interactions. The fields are all 4 vectors (co-vectors actually): the e-m potential A and Wa, a=1,2,3. SU(2) (just as SU(3) in QCD) enters through the adjoint representation of dimension 3.

One more time, why one claims that A and W are "unified", if the there's no single coupling constant and no global compact and connected gauge group which has the direct product U(1) x SU (2) as a subgroup?
 
  • #5
dextercioby said:
U(1) is the gauge group of electromagnetism, while SU(2)w is the gauge group of the weak interactions. The fields are all 4 vectors (co-vectors actually): the e-m potential A and Wa, a=1,2,3. SU(2) (just as SU(3) in QCD) enters through the adjoint representation of dimension 3.

One more time, why one claims that A and W are "unified", if the there's no single coupling constant and no global compact and connected gauge group which has the direct product U(1) x SU (2) as a subgroup?
Actually, U(1) is not the gauge group of electromagnetism and SU(2) is not the gauge group of the weak interaction. That was the point I wanted to make. That U(1) is the weak hypercharge, not the electromagnetic U(1). What happens is that electromagnetism corresponds to a linear combination of the weak hypercharge generator and of the ##T_3## diagonal generator of the weak isospin SU(2), so that the electric charge is given by ##Q = T_3 + Y/2 ## where (by abuse of notation) here ##T_3## is the eigenvalue of the diagonal generator of the weak isospin SU(2), and Y is the hypercharge. The orthogonal linear combination corresponds to the ##Z_0## boson while the ##T_\pm## correspond to the ##W^\pm##. It is in that sense that the weak interaction and the electromagnetic force are deeply linked. Now, you are right that they do not not have the same coupling constant since the coupling constants of the hypercharge U(1) and the weak isospin are not equal and this shows up through the Weinberg angle, so I agree with you that saying they are "unified" is a stretch. But they are definitely deeply linked together, in the sense I just described.
 
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  • #6
Thanks for pointing that essential aspect to me. Now I understand.
 
  • #8
dextercioby said:
U(1) is the gauge group of electromagnetism, while SU(2)w is the gauge group of the weak interactions

And there's your problem. That's a broken symmetry. The real U(1) x SU(2) has the U(1) of weak hypercharge and the SU(2) of weak isospin. The physical photons and W, Z's are mixtures of these two (and the Higgs)m, which is where unification comes in.
 
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Related to Explanation of terminology: electroweak

1. What does "electroweak" mean?

"Electroweak" refers to the unification of two fundamental forces in physics: electromagnetism and the weak nuclear force. This theory is a cornerstone of the Standard Model of particle physics.

2. How does the electroweak force work?

The electroweak force is mediated by four particles: the W+, W-, Z bosons, and the photon. These particles interact with particles that have electric charge and leptons, which are a type of fundamental particle.

3. What is the relationship between the electroweak force and the Higgs field?

The Higgs field is responsible for giving particles mass. In the electroweak theory, the Higgs field interacts with the W and Z bosons, giving them mass and allowing them to mediate the electroweak force.

4. How does the electroweak force relate to the other fundamental forces?

The electroweak force is one of the four fundamental forces in the universe, along with gravity, the strong nuclear force, and the weak nuclear force. It is responsible for interactions between charged particles and is closely related to the strong nuclear force.

5. What experimental evidence supports the electroweak theory?

There have been numerous experiments conducted, such as the discovery of the W and Z bosons at CERN in 1983, that have confirmed the predictions of the electroweak theory. Additionally, the precise measurements of the properties of these particles have further validated the theory.

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