# Self-interaction of gauge bosons in electroweak theory

As one learns in QFT, in Yang-Mills theories non-Abelian gauge transformations give rise to self-interactions of the gauge fields in the quadratic field strength term.

In QCD this produces the 3- and 4-gluon vertices. However, why don't we see the same in electroweak theory? Shouldn't there be 3- and 4-vertices of the weak gauge fields? That's what I would guess, since the $$SU(2)_L$$ part of the gauge group is non-Abelian. Or are those self-interactions somehow done away with via SSB?

• Like these? Aug 18, 2019 at 14:57
• en.wikipedia.org/wiki/Standard_Model#Gauge_bosons
– fqq
Aug 18, 2019 at 14:58
• Oh, so there are self-interactions. Well, that clears some things up. If someone puts that in an answer, I'll mark it as an answer. Aug 18, 2019 at 15:04

Electroweak theory does indeed have 3- and 4-gauge Boson vertices. For example, $$W^\pm$$ Bosons are charged, therefore couple to photons.

You can see the basic Feynman diagram vertices for electroweak and strong interactions on Wikipedia.