A symmetric model for leptons

In summary: In other words, the generators of the standard model must be in the LRS group in order to generate the quark masses.
  • #1
Shen712
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This is a homework problem in a course in particle physics at Cornell University.
Assume the Left Right Symmetric (LRS) model for leptons. The gauge group is GLR = SU(2)L×SU(2)R×U(1)X. The Standard Model group SU(2)L×U(1)Y has to be included in the LRS group. Namely, U(1)Y ⊂ SU(2)R×U(1)X. Find the linear combination of the LRS generators which gives the Standard Model generator Y.
The answer is: Y = T3R + X/2
How to get this result?
 
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  • #2
To give away the answer directly would violate Physics Forums rules. What are your own thoughts and what have you been able to conclude so far?
 
  • #3
Orodruin said:
To give away the answer directly would violate Physics Forums rules. What are your own thoughts and what have you been able to conclude so far?

My thoughts are: Since the SM generator Y is proportional to identity, the required linear combination of the LRS generators must also be proportional to identity. Considering that the generators of SU(2)R are TaR = τa/2, where τa are the Pauli matrices, only the combination of T3R and X is possible to be proportional to identity. Thus, Y = T3R + kX, where k is some constant. Since TaR = τa/2, if we take k = 1/2, we will get Y = τa/2 + X/2 = diag(1+X, -1+X)/2. This is a diagonalized matrix, but not proportional to identity. I am a little puzzled.
By the way, I am not a student at Cornell University, and this course is an old one in 2008. I just downloaded the course materials from the website and study them by myself. In this case, do the Physics Forum rules allow to give away the answer?
 
  • #4
Shen712 said:
In this case, do the Physics Forum rules allow to give away the answer?
No. We believe that regardless of whether you're doing an exercise as part of a course for credit, or for independent self-study, you're best served by figuring out the answer for yourself, with some help from hints and/or corrections as appropriate.
 
  • #5
I suppose that since you are looking at models beyond the standard model, you have already looked at the standard model itself... haven't you?
If yes, the problem is pretty much the same as the EM charge in the Electroweak theory: [itex]SU_L(2) \times U_Y(1) \rightarrow U_{Q}(1)[/itex].
 
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1. What is a symmetric model for leptons?

A symmetric model for leptons is a theoretical framework that attempts to explain the fundamental particles known as leptons through the use of symmetry principles. This model proposes that all leptons are composed of smaller, identical subunits and that their interactions are governed by symmetrical rules.

2. How does a symmetric model for leptons differ from other models?

Unlike other models that attempt to explain the properties of leptons, a symmetric model focuses on the underlying symmetry principles that govern the behavior of these particles. This approach allows for a more unified understanding of the different types of leptons and their interactions.

3. What evidence supports the existence of a symmetric model for leptons?

While there is currently no direct evidence for a symmetric model for leptons, the concept of symmetry has been proven to be a powerful tool in understanding the behavior of particles in the subatomic world. Additionally, the Standard Model of particle physics, which is the most widely accepted theory for describing the behavior of particles, is based on the principles of symmetry.

4. Are there any limitations to the symmetric model for leptons?

As with any scientific theory, there are limitations to the symmetric model for leptons. One limitation is that it does not account for the observed differences in mass between different types of leptons. Additionally, the model does not currently provide a complete explanation for all of the observed properties and behaviors of leptons.

5. How does a symmetric model for leptons contribute to our understanding of the universe?

The symmetric model for leptons is a crucial component of the larger Standard Model of particle physics, which is considered to be the most successful and comprehensive theory for describing the behavior of particles. By providing a deeper understanding of the fundamental building blocks of matter, the symmetric model for leptons contributes to our understanding of the fundamental laws that govern the universe.

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