| A field is completely determined by the existence of a vector potential and a scalar potential. The quanta of a vector potential are the charges of that field and the quanta of a scalar potential are the masses of that field. And the finiteness of charge and mass fixes the maximum number of fundamental particles. These charge and mass are the detectable things for experiments.
For the electromagnetic field, the symmetry is U(1).
For the electroweak field, the symmetry is SU(2).
For the QCD or strong color field, the symmetry is SU(3). |