In non-abelian gauge theories self interaction of gauge fields is permitted, all
ID: 1391666 • Letter: I
Question
In non-abelian gauge theories self interaction of gauge fields is permitted, allowing coupling such as WWZ (i.e. Z-boson decaying to W+W?) or ggg (i.e. gluon splitting into two new gluons).
The aforementioned particles are spin-1 particles, thus I'd assume that the above processes are prohibited from spin considerations. Consider for example a spin +1 gluon splitting in two new gluons, their total spin can either add to +2 or 0.
I am well aware that spin itself is not conserved in these interactions but only the total angular momentum J=S+L, thus I'd assume that the two gluons have a nonzero relative angular momentum L.
My question is whether that is the correct explanation for the phenomenon. My QM skills are a little bit rusty, so any help is appreciated!
Explanation / Answer
The massive verse massless cases are different.
Massive vector bosons are a bit more 'honest' in their representation of the Lorentz group in that they have all 3 DOF implied by the j=1 representation. That is, they have 2j+1=2(1)+1=3 states with j=?1,0,+1 angular momentum. So now you can see that you can have 2 massive vector bosons one with j=+1 , the other with j=?1 that goes to a j=0 state (with other possibilities as well).
Massless vector bosons only have the two j=
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