Possibility of gauge independence of wave-function renormalization constants is studied on the basis of gauge-field theories with gauge covariance. By the use of the expression for the double-pole type propagator DF(x) [DDF(x) =DF(x)], exploited by Zwanziger, it is asserted that DF(O) can be consistently taken to be zero. As a consequence, all renormalization constants become gauge independent within the framework of formalisms adopted.
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