Eigenvalues of J_2 + K_1; -J_1 + K_2

[wandering.the.cosmos]

Weinberg in volume 1 of his QFT text says we do not observe any non-zero eigenvalues of $A = J_2 + K_1; B = -J_1 + K_2$. He says the "problem" is that any nonzero eigenvalue leads to a continuum of eigenvalues, generated by performing a spatial rotation about the axis that leaves the standard vector invariant.

What are the observable consequences of non-zero eigenvalues of A and B?

 

[alphaone]

Very interesting question to which I unfortunately do not know an answer. But I agree that it is very unsatisfying to argue along the usual lines that no continuous degree of freedom is observed experimentally for massless paricles and then concluding that therefore A and B have to be 0. It would be much more satisfying if we could get this result out of theoretical physics without referring to experiment but unfortunately I have not heard of any such argument, so if anybody knows one I would be delighted to hear about it.