Understanding the Higgs Mechanism

[touqra]

Let me take an example.
Suppose we have a Lagrangian, of a scalar field coupled to itself and a massless gauge boson field. Next, we expand the Lagrangian about the vacuum expectation value of the scalar field, and it turns out that, in the end, the gauge boson is massive.
My question is, this massive boson has a mass in the vicinity of the scalar field's VEV. But if we expand the scalar around some other values, the mass of the gauge boson changes too. And we can also expand the Lagrangian around some scalar value, such that the gauge boson remains massless...

 

[RafaMarce]

I think "yes", we have to choose the point where all fields vanish to do the expansion of lagrangean... There is a possible vacuum state in this point. But this is a trivial solution, i think is the only place where we have massless gauge boson, since that the symmetry is broken.