Local Gauge Invariance of Non-Abelian Gauge Field Theory

The non-abelian guage field theory is formulated under a gauge fixing condition of non-differential form. The condition is characterized by two properties: (i) Time-like components of gauge fields are completely determined by the other components and source fields, as in the radiation gauge. (ii) Gauge functions are timely constant arbitrary functions, and then independent of field operators. The theory is proved to be “form-invariant” under local gauge transformations. Our formulation can be regared as a legitimate formulation of an expedience in the radiation gauge formulation, where the field operator dependence of gauge functions is completely disregarded. Property (ii) makes our formulation deviate from the radiation gauge formulation to a large extent.