  Many transport coefficients of the quark-gluon plasma and nuclear structure
functions can be written as gauge invariant correlation functions of
non-Abelian field strengths dressed with Wilson lines. We discuss the
applicability of axial gauge $n\cdot A=0$ to calculate them. In particular, we
address issues that appear when one attempts to trivialize the Wilson lines in
the correlation functions by gauge-fixing. We find it is always impossible to
completely remove the gauge fields $n\cdot A$ in Wilson lines that extend to
infinity in the $n$-direction by means of gauge transformations. We show how
the obstruction appears in an explicit example of a perturbative calculation,
and we also explain it more generally from the perspective of the path integral
that defines the theory. Our results explain why the two correlators that
define the heavy quark and quarkonium transport coefficients, which are
seemingly equal in axial gauge, are actually different physical quantities of
the quark-gluon plasma and have different values. Furthermore, our findings
provide insights into the difference between two inequivalent gluon parton
distribution functions.
