Gauge eigenstates vs. Mass eigenstates

In summary: Thanks for the answer!I think you're right, the fermions do seem to be eigenvectors of some operator related to the gauge group. I am not too sure about the gauge bosons though.
  • #1
Kontilera
179
23
Hello fellow physicsforumists.
I am currently looking at the standard model and one of the key ingridients is to rotate the gauge eigenstates to the mass eigenstates by a transformation acting on their family index. The problem is that I can't really see what we are doing.

The mass eigenstates are such that the massterm coefficients matrices are diagonal. But how do we define gauge eigenstates to begin with?

Please, if you have the energy to write some word about this I would be thankful.

Best Regards
Kontilera
 
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  • #3
gauge eigenstates are unphysical.Each quark in standard model has right handed components because they are massive.Lagrangian is first written in terms of the doublet and singlet fields which contain these unphysical quarks which are termed as gauge quarks or sometimes gauge eigenstates.When you use yukawa coupling to give masses to quarks,a mass matrix is generated.these determine the masses and flavour mixing of quarks.The quark fields used before(SSB) are unphysical gauge eigenstes,you have to find the physical or mass eigenstates by transforming the quark mass matrices into diagonal form.
 
  • #4
The unphysical gauge eigenstates are defined based on the other fields that will be connected to it through the gauge interaction, so for instance there is a term like uwd' in the Lagrangian which represents the interaction of a u quark with a W boson and a d' unphysical quark. The d' along with the s' and d' can be related to the physical (mass eigenstates) fields d, s, and b through a "rotation".
 
  • #5
Thanks for the answers. I helped me some but I'm not sure I understand why they are referred to as gauge eigenstates.. is there an eigenvalue equation?
 
  • #6
Kontilera said:
Thanks for the answers. I helped me some but I'm not sure I understand why they are referred to as gauge eigenstates.. is there an eigenvalue equation?
They are more commonly referred as gauge quarks,gauge eigenstate is just misnomer.They are written like like that because they relate to physical mass eigenstates.
 
  • #7
Kontilera said:
Thanks for the answers. I helped me some but I'm not sure I understand why they are referred to as gauge eigenstates.. is there an eigenvalue equation?

andrien said:
They are more commonly referred as gauge quarks,gauge eigenstate is just misnomer.They are written like like that because they relate to physical mass eigenstates.

I'm a little rusty on my group theory, but I don't think it's a misnomer. The relevant eigenvalue equations are the ones where the operator is a Cartan generator of one of the gauge groups right? Or some such thing. For instance if we consider SU(2), then before symmetry breaking the 3 (massless) gauge bosons are eigenvectors of the diagonal SU(2) generator, in the 3x3 (I think this is the adjoint?) representation. Similarly the left handed (massless) fermions are eigenvectors of the same generator but in the 2x2 (fundamental?) representation.
 
  • #8
Err actually maybe it is only the fermions that work like that; I am pretty sure they at least are all eigenvectors of some gauge-group related operator or another.
 

What is the difference between gauge eigenstates and mass eigenstates?

Gauge eigenstates and mass eigenstates are two different types of states that can describe the properties of a physical system. Gauge eigenstates refer to the states that are used to describe the interaction between particles and the fundamental forces of nature, such as electromagnetism or the strong and weak nuclear forces. Mass eigenstates, on the other hand, refer to the states that describe the mass and energy of particles. In other words, gauge eigenstates describe how particles interact with the environment, while mass eigenstates describe the internal properties of the particles themselves.

How are gauge eigenstates and mass eigenstates related?

Gauge eigenstates and mass eigenstates are related through a mathematical process called diagonalization. This process involves transforming the equations that describe the gauge eigenstates into equations that describe the mass eigenstates. In other words, it allows us to find the mass eigenstates that correspond to a given set of gauge eigenstates. This is important because the mass eigenstates are the states that we can measure in experiments, while the gauge eigenstates are more abstract mathematical constructs.

Why is it important to distinguish between gauge eigenstates and mass eigenstates?

It is important to distinguish between gauge eigenstates and mass eigenstates because they have different physical interpretations and applications. Gauge eigenstates are used to understand the fundamental interactions between particles, while mass eigenstates are used to describe the properties of particles themselves. Additionally, the transformation between gauge eigenstates and mass eigenstates is essential for making accurate predictions in particle physics experiments.

Do all particles have both gauge eigenstates and mass eigenstates?

No, not all particles have both gauge eigenstates and mass eigenstates. Some particles, such as photons, only have gauge eigenstates because they do not have mass. On the other hand, particles like quarks and electrons have both gauge eigenstates and mass eigenstates because they have both mass and interact with the fundamental forces.

Can gauge eigenstates and mass eigenstates change over time?

Yes, gauge eigenstates and mass eigenstates can change over time. This is because particles can interact with other particles or fields, causing their properties to change. For example, a particle may start off in a certain mass eigenstate but then interact with a Higgs field, causing it to change to a different mass eigenstate. Similarly, gauge eigenstates can change due to interactions with other particles or fields, causing their properties to evolve over time.

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