On one hand, in reading Georgi's book in group theory, I comprehend the invariant tensor as a special "tensor", which is unchanged under the action of any generators. On the other hand, CG decomposition is to decompose the product of two irreps into different irreps.
Now it is claimed that...
In demonstrating that Higgs mechanism gives mass to gauge boson fields, we used the fact that hypercharge Y=1/2, which is due to "Higgs particle is a complex doublet of the weak isospin SU(2) symmetry". But why?
In other words, can you show the details about why the Higgs field has charge...
I am studying QFT and got stuck on one question which may be simple. Why is structure constants (in Lie algebra) real and independent on representations? Can you give me a detailed proof?
Thanks!