Why gauge symmetry?

Abstract

It is argued that the Weinberg-Salam model is the way it is because the most general self-consistent effective field theory of massive vector bosons interacting with fermions and photons at leading order coincides with the Weinberg-Salam model in unitary gauge where the scalar field is replaced by its vacuum expectation value. To support this argument the most general Lorentz-invariant effective Lagrangian of massive vector bosons coupled to massless fermions is considered. Restrictions imposed on the interaction terms following from the consistency with the constraints of the second class and the perturbative renormalizability in the sense of effective field theories is analyzed. It is shown that the leading order effective Lagrangian containing interaction terms with dimensionless coupling constants coincides with the leading order effective Lagrangian of the locally invariant Yang-Mills theory up to globally invariant mass term of the vector bosons. Including the fermion masses and mixings and the interaction with the electromagnetic field leads to an effective field theory which at leading order looks like as if it was an $SU(2)\times U(1)$ gauge invariant theory with spontaneous symmetry breaking in unitary gauge with the scalar field replaced by its vacuum expectation value.