SU(2)L, SU(2)R, other symmetric groups and SSB

In summary, the conversation discusses the SU(2)L, SU(2), and SU(2)R groups and their importance in electroweak interactions. The difference between these groups and their role in the Lagrangian is also mentioned. The concept of spontaneous symmetry breaking and the appearance of a Higgs field is brought up, along with the change in symmetry from SU(2)L x SU(2)R to SU(2)L+R. The question of how to determine which symmetries will survive when symmetry is spontaneously broken is also raised. The book "Srednicki" is recommended as a resource for further understanding.
  • #1
Anne-Sylvie
12
0
Hello everyone,

When we speak about the SU(2)L group (in electroweak interactions for example), about what group do we talk ? What is the difference with the SU(2) group ? And with the SU(2)R ? Why is the label so important ?

I ask this because I see that a Lagrangien can be invariant under SU(2)L x SU(2)R. I think that means that if we apply any transformation of the SU(2)L and then SU(2)R on the lagrangien, it will give the same lagrangien as before. Is it right ?
Then, when we consider the Higgs mechanism. There is an non zero expectation value, and then via the spontaneous symmetry breaking mechanism, a higgs field appear, etc, and we have another lagrangien. This lagrangien is no longer invariant under SU(2)L x SU(2)R transformations, but well under SU(2)L+R. What does that mean ? What is SU(2)L+R ? How can we know, when we spontaneously break a symmetry, which symmetries will survive ?

I'm a bit confused with all of that. I hope I'm relatively clear in my message... Please excuse me for my English but I'm non native and I'm still learning this usefull langage. :-)
 
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  • #2
See chapters 83, 88, and 89 in the book by Srednicki (draft version freely downloadable at his web page).
 
  • #3
Thanks for your advice. :-)
 

1. What are SU(2)L and SU(2)R?

SU(2)L and SU(2)R are groups in theoretical physics known as gauge groups. They represent the symmetries of the weak nuclear force and are associated with left- and right-handed particles, respectively. These groups are part of the Standard Model of particle physics.

2. What is the significance of these groups in particle physics?

These groups play a crucial role in the theory of electroweak interactions, which describes the unified theory of the electromagnetic and weak nuclear forces. They also play a role in the Higgs mechanism, which is responsible for the generation of mass in particles.

3. What other symmetric groups are important in particle physics?

In addition to SU(2)L and SU(2)R, other important symmetric groups in particle physics include SU(3) and U(1). SU(3) is associated with the strong nuclear force and U(1) is associated with the electromagnetic force.

4. What is spontaneous symmetry breaking (SSB)?

SSB is a phenomenon in which the symmetry of a system is broken at lower energy levels. In particle physics, it is a crucial concept in understanding the origin of mass and the Higgs mechanism. It also plays a role in the theory of phase transitions in condensed matter systems.

5. How does SSB relate to the Higgs mechanism?

The Higgs mechanism involves the spontaneous breaking of the SU(2)L and U(1) symmetry in the Standard Model. This results in the creation of a new field (the Higgs field) and the associated Higgs boson, which gives mass to particles that interact with it. SSB plays a crucial role in this mechanism by breaking the symmetry and allowing for the generation of mass.

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