In the standard model, the Lagrangian contains scalar and spinor and vector fields. But when we consider spontaneous symmetry breaking, we only account for the terms contain only scalar fields, " the scalar potential", in the Lagrangian. And if the scalar fields have vacuum expectation value, then we recognize the symmetry is broken spontaneously. Why don't we have to contain spinors and vectors? I think it's related to Lorentz invariance.