Gauge-invariant proper self-energies and vertices in gauge theories with broken symmetry

Using the pinch technique, we show how to recover, from the $S$ matrix of a spontaneously broken non-Abelian gauge theory, proper self-energies and vertices which are fully gauge invariant when one or more momenta are off shell. Explicit calculations are carried out at the one-loop level for gauge-boson self-energies and fermion-gauge-boson vertices in a simple SU(2) gauge theory with a Higgs boson. The same technique allows us to calculate, at one-loop order, a neutrino electromagnetic form factor which is gauge invariant at all photon momenta, thus resolving a long-standing problem. We show how massless Goldstone bosons, not present in the $S$ matrix, must be introduced into Green's functions in order to reconcile gauge invariance and renormalizability.