  We demonstrate that pure space-like axial gauge quantizations of gauge fields
can be constructed in ways which are free from infrared divergences. We begin
by constructing an axial gauge formulation in auxiliary coordinates:
$x^+=x^0\sin{\theta}+x^1\cos{\theta}, x^-=x^0\cos{\theta}-x^1\sin{\theta}$. For
\theta less than \pi\over 4 we can take $x^-$ as the evolution parameter and
construct a traditional canonical formulation of the temporal gauge Schwinger
model in which residual gauge fields dependent only on $x^+$ are static
canonical variables. Then we extrapolate the temporal gauge operator solution
into the axial region, \theta > \pi \over 4, where $x^+$ is taken as the
evolution parameter. In the axial region we find that we have to change
representations of the residual gauge fields from one realizing the PV
prescription to one realizing the ML prescription in order for the infrared
divergences resulting from $({\partial}_-)^{-1}$ to be canceled by
corresponding ones resulting from the inverse of the hyperbolic Laplace
operator. Finally, by taking the limit ${\theta}\to\frac{\pi}{2}-0$ we obtain
an operator solution and the Hamiltonian of the axial gauge (Coulomb gauge
)Schwinger model in ordinary coordinates. That solution includes auxiliary
fields and the representation space is of indefinite metric, providing further
evidence that ``physical'' gauges are no more physical than ``unphysical''
gauges.
