INTERNAL CHARGE OF GAUGE FIELD

The internal charges of the non-Abelian gauge field are investigated on the classical level. Restrictions which insure that the definition of the internal charges is geometrically meaningful and relativistically invariant are employed to determine their physical nature. The possibility for the geometric breaking of the global conservation laws of the covariant divergence free currents is shown not to exist: their charges if defined and comparable at in and out states are also conserved. It is found that for localized external sources and gauge fields only one of the currents, the Yang-Mills current, leads to a nonvanishing total charge. A gauge-invariant definition is given for the internal charge carried by the gauge field itself. It is shown that the components of the gauge field giving rise to the internal charge satisfy Maxwell's equations either everywhere or at large distances from the source region. This indicates that the gauge field can account only for electric charge. © 1968.