Abstract
A generating functional to be used for calculating gauge-invariant Green's functions of a non-Abelian gauge theory is constructed in terms of an unconstrained external current. This functional is a singular distribution and so must be treated as the limit of a well-defined functional, one particular choice of which is that for a massive gauge theory as the mass goes to zero. It is suggested that the gauge-invariant Green's functions so obtained may be smooth in this limit.
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