# Attempts to explain Higgs coupling as a gauge transformation symmetry

As is (supposedly) well known, Electromagnetic coupling can be "explained" as a closure term to a langrangian comprising a free Dirac field and a free vector field that are required to be invariant under transformations that add arbitrary gradient quantities to the vector field and matching local phase $U(1)$ adjustments to the Dirac field, a construction better known as gauge invariance.

There are similar gauge invariant arguments to obtain the electro-weak and chromodynamic couplings. None of such applies so far to gravity in a way that is entirely satisfactory (to me, yes), specially with all the non-sense that its straightforward application would imply (such as no local observables, etc.)

This particular question is about the Higgs field; from my understanding it is entirely added by hand to all (or most?) fermion fields. It couples also to gauge vector bosons but unlike those, i've never seen any allegations that such coupling would arise naturally from a gauge invariance schema. Are there any attempts to produce any of such constructions that is worth mentioning?

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The standard model Higgs coupling to electroweak vector bosons does arise from local gauge invariance (combined with spontaneous symmetry breaking), but the couplings to fermions have to be inserted by hand AFAIK. Is that what you're asking about? I can post an answer if that's what you're asking about, but you might want to read this one first. – David Z Feb 21 '12 at 20:05
I think the problem is that the symmetry that is "broken" by the Higgs mechanism (i.e. the famous "Mexican hat potential" symmetry) is neither local nor global symmetry. It is a symmetry at a single point $\phi=0$. – Murod Abdukhakimov Feb 22 '12 at 9:37
@DavidZaslavsky, i appreciate the answer you linked, it is very good, +1, However i was referring concretely to the part of the coupling that is added by hand, which is the fermionic coupling – lurscher Feb 22 '12 at 20:35
OK, I see. In the last paragraph of your question you wrote that the coupling is added by hand to gauge vector bosons as well as fermion fields, so I wanted to clarify whether you were asking about the origin of only the fermion couplings or of all the couplings. (Perhaps you could edit the question to make it clear you're asking about fermions only?) In the latter case I could have posted an answer, but as it is, I don't know that much about the state of attempts to produce the fermion couplings from gauge invariance. I think supersymmetry tends to do more in that area. – David Z Feb 22 '12 at 20:45
thanks, hope the edit makes it more clear – lurscher Feb 22 '12 at 20:51