What is isospin (and spin) really

[KBriggs]

My question is simple, though the answer is probably not. What is isospin? (Here, I refer to the strong isospin introduced by Cassen and Condon).

From the algebra it is clear that there are analogies to be drawn with the intrinsic spin that arises in angular momentum conservation, but how far can the analogy be pushed. Can we say that isospin is a generalized angular momentum intrinsic to particles in strong interactions?

From the spin of an electron, the usual picture is that the electron is spinning (though the classical picture breaks down quite quickly if you try to push that too far). How is that similar (and more importantly, how is that different) from a laymen's definition of isospin?

Thanks for your time

 

[humanino]

The similarity (or mathematical identity) between the algebras is as far as the analogy can be drawn, and explains the origin of the name. The isospin value is not a reflection of a given angular momentum (spin).

"Spin" refers to the transformation properties of the representation (of the Lorentz group) to which a particle belongs when performing a spacetime rotation. The axis of this (mathematical) space are time and (ordinary) spatial directions. The transformations are special unitary. I hope it does not sound too complicated, it really is jargon. There is a stack of complex numbers which turn into one another when we perform spatial rotations, just as would happen for the real numbers forming an ordinary position vector, or a momentum vector, in a different physical case than position or momentum.

"Isospin" refers to the same story, in a space which now have quark flavors along its directions. So you can have an isospin multiplet defined for proton and neutron (both are spin 1/2), or for positive, neutral and negative pions (scalars, spin 0). Isospin is the simplest case in which we built isospin representation out of just u and d flavors. You can get "generalized" isospin by including more flavors.

You can take a look at the "baryonic periodic tables" we get playing these classification games here

 

[naima]

hello Humanino

We are happy to see that you still find time to be on the forum.
just one question:
Is still "strong isospin' used or was it replaced by "weak isospin"?

 

[KBriggs]

Thanks for your reply :)

So isospin is essentially a quantity that is used to label particles, which behaves algebraically like a generalized angular momentum in that it satisfies the algebraic requirements, but physically it cannot be considered to be angular momentum in usual space-time (in particular, has nothing to do with angular momentum conservation in the usual sense of the phrase).

One more question for you. Most references about isospin refer to it as "isobaric" spin at some point, without clarifying what isobaric means in this context. Could you shed some light on that term as well?

 

[naima]

isobaric comes from greek iso (same) and baros (weight)
neutron and proton have almost the same mass and are grouped in a isobaric doublet.