SU(2)xU(1) Unification: Exploring Weak & Electromagnetic Interactions

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In summary, when a model is SU(2)xU(1), it means that the fields or particles of the model form a representation of the direct product group SU(2)XU(1) and this group is used to unify electromagnetism and the weak interaction. The SU(2) symmetry is similar to rotations in 3D while the U(1) symmetry is about phase changes. In the electroweak theory, the W and B fields mix to form Z and photon, which allows for flavor-changing-neutral-currents and operates on electric charge. Combining the non-Abelian SU(3) QCD gluons into the mix leads to a GUT and a possible TOE. When a particle
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Magister
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What does it mean to have a model that is SU(2)xU(1)? Does it have anything to do with the electro-weak unification? I asking this because the weak interaction has 2 bosons and the electromagnetic interaction has 1 boson... :confused:
 
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  • #2
Magister said:
What does it mean to have a model that is SU(2)xU(1)?
It means that the fields (particles) of your model form a representations (multeplets) of the (direct product) group SU(2)XU(1).

Does it have anything to do with the electro-weak unification?

Yes, SU(2)XU(1) is the group used by Wienberg & Salam to unify electromagnatic interaction with the weak interaction.

I asking this because the weak interaction has 2 bosons

NO, there are three weak bosons [itex]W^{\pm},Z^{0}[/itex].
Clearly, you need to know something about group theory.

regargs

Sam
 
  • #3
I guess the easiest way to understand this is to say that a theory is U(1)xSU(2) if it symetric under an U(1) symetry and a SU(2) symetry.
An U(1) symetry is just a phase change some [TEX]exp(i*\phi)[\TEX] multiplication that leaves the overall phase unchanged is a very common symetry e.g. the symetry of electromagnetism.
The SU(2) symetry is a bit more abstract it´s very similar to an SO(3) symetry e.g. a symetry under rotations in 3D, you can read about that in many representation theory books.

This symetry could be about the mixing of two particles for example e.g. you change the
Amplitude for two particles beeing in a state where their amplitudes for manifestation are equal to one where one dominates or something.

I guess this would be the most elementary idea i guess it would be best if you start of with some good intro to classical mechanics and look up the noether stuff if you didn´t allready do that :)
 
  • #4
Mr.Brown said:
This symetry could be about the mixing of two particles for example e.g. you change the
Amplitude for two particles beeing in a state where their amplitudes for manifestation are equal to one where one dominates or something.

I guess this would be the most elementary idea i guess it would be best if you start of with some good intro to classical mechanics and look up the noether stuff if you didn´t allready do that :)

And in electroweak theory, it sort of is. You have the W1, W2, W3, and B fields, where B operates only on hypercharge, and W3 only on isospin. What happens is that W1 and W2 mix to form W+ and W-, and W3 and B mix to produce Z and photon. W3 and B are both very massive, but the mixing to Z and photon leaves us with extremely massive Z and massless photon. The new fields Z and photon operate on linear combinations of hypercharge and isospin, giving us a Z boson that allows flavor-changing-neutral-currents and a photon that only operates on electric charge (which, itself, is a linear combination of hypercharge and isospin) in the Abelian sense.

The challenge now is to combine the non-Abelian SU(3) QCD gluons into the mix. If this can be done, it will give us a GUT, and adding gravitation would represent a possible TOE. If it can even be done (still debatable, I think).
 
  • #5
Yeah i guess Coleman-Mandula-Weinberg puts some pretty servery restrictions on what can be done and what can´t.
 
  • #6
I have being studying group theory but I am getting to it quite slowly. Please correct me if I am wrong. When we say that a particle theory is invariant for a given group we are saying that the particles form a representation of that group. So for instance the leptons doublets forms a representation of the SU(2) group and the photon a representation of the U(1) group.

Now I am asked to study the SU(2)xU(1)x[itex]S_3[/itex] lepton doublets unification (more precisely the paper of E. Derman, "Flavor unification, tao decay and b decay within the six-quark-six-lepton Weinberg-Salam model" Phys. Rev. D 19 (1979)). I am asked to write the Higgs potential (eq. 4.1 of that paper) in a new invariant subspace of [itex]S_3[/itex] and this is freaking me out. I make no idea where to start! I just can't make the connection between the particles doublets and the vector basis of the invariant subspace.

Thanks for any help.
 
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  • #7
Where can I learn more about doublet representation? Are the doublet and spinor representations the same?
 
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1. What is the significance of SU(2)xU(1) unification in particle physics?

SU(2)xU(1) unification is a crucial concept in particle physics as it aims to explain the fundamental forces of nature, specifically the weak and electromagnetic interactions. This unification theory proposes that these two forces are actually different manifestations of a single unified force at very high energies. It provides a deeper understanding of the underlying structure of the universe and has been extensively studied and tested by scientists.

2. How does SU(2)xU(1) unification work?

SU(2)xU(1) unification works by combining the gauge symmetries of the SU(2) and U(1) groups. SU(2) represents the weak force, which is responsible for radioactive decays, while U(1) represents the electromagnetic force, responsible for interactions between electrically charged particles. By combining these two symmetries, the unification theory proposes that at high energies, these two forces are indistinguishable and become a single unified force.

3. What evidence supports the SU(2)xU(1) unification theory?

There is strong evidence to support the SU(2)xU(1) unification theory, including the discovery of the W and Z bosons, which are predicted by the theory. The Standard Model of particle physics, which successfully describes the interactions between particles and forces, is also based on SU(2)xU(1) unification. Additionally, experiments at high energy particle accelerators, such as the Large Hadron Collider, have observed interactions between particles that are consistent with the predictions of the theory.

4. What are the implications of SU(2)xU(1) unification for our understanding of the universe?

The unification of the weak and electromagnetic forces through SU(2)xU(1) has significant implications for our understanding of the universe. It provides a more complete picture of the underlying structure of matter and forces, and opens up possibilities for further unification with other fundamental forces, such as gravity. It also helps to explain the symmetry and balance observed in the laws of nature.

5. Are there any challenges or limitations to the SU(2)xU(1) unification theory?

While the SU(2)xU(1) unification theory has been successful in explaining and predicting many phenomena in particle physics, it is not without its challenges and limitations. One limitation is that it does not include gravity, which is still not fully understood in the context of the other fundamental forces. Additionally, the theory has not yet been fully integrated with quantum mechanics, which is necessary for a complete understanding of the universe. Scientists continue to explore and refine the unification theory in order to address these challenges and limitations.

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