Undergrad Do the SU(n) generators represent any observables?

[tomdodd4598]

Hey there,

I've recently been trying to get my head around Yang-Mills gauge theory and was just wandering: do the Pauli matrices for su(2), Gell-Mann matrices for su(3), etc. represent any important observable quantities? After all, they are Hermitian operators and act on the doublets and triplets of the theories, but have bizarre eigenvalues that I can't get my head around. If so, what are they, and if not, why not? What about the adjoint operators?

Thanks in advance :)

 

[dextercioby]

In Quantum Field Theory, "observables" really stands for something (mathematical quantity) which can be measured in the lab. Scattering cross sections or scattering probabilities are the observables of the theory. Matrices (Pauli, Dirac, Gell-Mann) are just calculation input parameters.

 

[tomdodd4598]

Matrices (Pauli, Dirac, Gell-Mann) are just calculation input parameters.

Ok, perhaps I should ask a slightly different question then - are the eigenvalues and eigenvectors of these matrices important? Do they not tell us anything useful about the structure of the theory, and do they not tell us about weak isospin, hypercharge, colour charge, etc? Forgive me if I'm barking up the wrong tree.