The Higgs mechanism spontaneous breaking of a local gauge symmetry (simplest U(1) gauge symmetry) procedure: add the Higgs potential to Lagrangian translate the field to a true ground state obtained particle spectrum: 1 Higgs field with mass 1 massive vector A  - desired 1 massless Goldstone boson - unwanted with a special choice of gauge the unwanted Goldstone boson becomes longitudinal polarization of the massive vector  the Higgs mechanism has avoided massless particles
{}