  Evaluation of variation of a Green's function in a gauge field theory with a
gauge parameter theta involves field transformations that are (close to)
singular. Recently, we had demonstrated {hep-th/0106264}some unusual results
that follow from this fact for an interpolating gauge interpolating between the
Feynman and the Coulomb gauge (formulated by Doust). We carry out further
studies of this model. We study properties of simple loop integrals involved in
an interpolating gauge. We find that the proof of continuation of a Green's
function from the Feynman gauge to the Coulomb gauge via such a gauge in a
gauge-invariant manner seems obstructed by the lack of differentiability of the
path-integral with respect to theta (at least at discrete values for a specific
Green's function considered) and/or by additional contributions to the
WT-identities. We show this by the consideration of simple loop diagrams for a
simple scattering process. The lack of differentiability, alternately, produces
a large change in the path-integral for a small enough change in theta near
some values. We find several applications of these observations in a gauge
field theory. We show that the usual procedure followed in the derivation of
the WT-identity that leads to the evaluation of a gauge variation of a Green's
function involves steps that are not always valid in the context of such
interpolating gauges. We further find new results related to the need for
keeping the epsilon-term in the in the derivation of the WT-identity and and a
nontrivial contribution to gauge variation from it. We also demonstrate how
arguments using Wick rotation cannot rid us of these problems. This work brings
out the pitfalls in the use of interpolating gauges in a clearer focus.
