  It is shown that ghost fields are indispensable in deriving well-defined
antiderivatives in pure space-like axial gauge quantizations of gauge fields.
To avoid inessential complications we confine ourselves to noninteracting
abelian fields and incorporate their quantizations as a continuous deformation
of those in light-cone gauge. We attain this by constructing an axial gauge
formulation in auxiliary coordinates $x^{\mu}= (x^+,x^-,x^1,x^2)$, where
$x^+=x^0{\rm sin}{\theta}+x^3{\rm cos}{\theta}, x^-=x^0{\rm
cos}{\theta}-x^3{\rm sin}{\theta}$ and $x^+$ and $A_-=A^0{\rm cos}
{\theta}+A^3{\rm sin}{\theta}=0$ are taken as the evolution parameter and the
gauge fixing condition, respectively. We introduce $x^-$-independent residual
gauge fields as ghost fields and accomodate them to the Hamiltonian formalism
by applying McCartor and Robertson's method. As a result, we obtain conserved
translational generators $P_{\mu}$, which retain ghost degrees of freedom
integrated over the hyperplane $x^-=$ constant. They enable us to determine
quantization conditions for the ghost fields in such a way that commutation
relations with $P_{\mu}$ give rise to the correct Heisenberg equations. We show
that regularizing singularities arising from the inversion of a hyperbolic
Laplace operator as principal values, enables us to cancel linear divergences
resulting from $({\partial}_-)^{-2}$ so that the Mandelstam- Leibbrandt form of
gauge field propagator can be derived. It is also shown that the pure
space-like axial gauge formulation in ordinary coordinates can be derived in
the limit ${\theta}\to\frac{\pi}{2}-0$ and that the light-cone axial gauge
formulation turns out to be the case of ${\theta}=\frac{\pi}{4}$.
