How Do Spin, Isospin, and Charges Interact in Particle Physics?

[kith]

Recently, I was thinking about spin and isospin. It's been a while since I've dealt with particle physics, so my knowledge may be a bit rusty.

In the Standard Model, we have three interactions with associated coupling constants e, g_w and g_s. A particle may have three different charges Q_e, Q_w, Q_s which are multiples of e, g_w and g_s. Also we have three types of spin -"ordinary" spin, weak isospin, strong isospin- and their projections S₃, T₃ and I₃.

These spin projections are related to the interactions but it isn't a one-to-one correspondence. Neutrinos for example have Q_e=0 but S₃ = ±1/2 and the weak isospin depends on Q_e. Does this mixing of interactions only reflect the fact that we need the unified electroweak theory to explain some experimental facts or is there more to it?

Also, are the spin projections together equivalent to the charges? If yes, what is the idea of these different concepts and when do we use which one? If no, what's the difference between them?

Thanks
kith

 

[AndyW]

Dear kith,

Thank you for your question. Spin and isospin are important concepts in particle physics, and understanding their relationship to interactions is crucial in understanding the Standard Model.

Firstly, it is important to note that spin and isospin are not the same thing. Spin is an intrinsic property of particles, similar to mass and charge. It is a quantum mechanical property that describes the rotational behavior of particles. Isospin, on the other hand, is a mathematical construct used to describe the strong nuclear force.

In the Standard Model, we have three fundamental interactions - electromagnetic, weak, and strong. These interactions are described by coupling constants, which determine the strength of the interaction. As you mentioned, particles can have different charges associated with these interactions, which are multiples of the coupling constants.

The concept of isospin was introduced to explain the symmetries observed in the strong nuclear force. It is a mathematical tool used to describe the interactions between particles with different charges. It is similar to spin, but instead of describing rotational behavior, it describes the behavior of particles under strong interactions.

The mixing of interactions that you mentioned is a result of the unification of the electromagnetic and weak forces in the electroweak theory. This theory explains the experimental fact that the weak interaction appears to violate parity symmetry, while the electromagnetic interaction does not. This is because the weak interaction only interacts with particles with left-handed spin, while the electromagnetic interaction interacts with both left- and right-handed particles.

As for the relationship between spin projections and charges, they are not equivalent. Spin projections are related to the intrinsic properties of particles, while charges are associated with their interactions. However, in certain cases, the spin projections and charges may have the same numerical values, such as in the case of the neutrino.

In summary, the concepts of spin and isospin are important in understanding the fundamental interactions in the Standard Model. They are not the same thing, but they are related and play crucial roles in explaining the behavior of particles. I hope this helps clarify some of your questions.