  We construct a new perturbative formulation of pure space-like axial gauge
QED in which the inherent infrared divergences are regularized by residual
gauge fields. For that purpose we perform our calculations in coordinates
$x^{\mu}=(x^+,x^-,x^1,x^2)$, where $x^+=x^0\sin{\theta}+x^3\cos {\theta}$ and
$x^-=x^0\cos{\theta}-x^3\sin{\theta}$. $A_-=A^0\cos{\theta}+A^3
\sin{\theta}=n{\cdot}A=0$ is taken as the gauge fixing condition. We show in
detail that, in perturbation theory, infrared divergences resulting from the
residual gauge fields cancel infrared divergences resulting from the physical
parts of the gauge field. As a result we obtain the gauge field propagator
prescribed by Mandelstam and Leibbrandt. By taking the limit $\theta {\to}
\frac{\pi}{4}$ we can construct the light-cone formulation which is free from
infrared difficulty. With that analysis complete, we perform a successful
calculation of the one loop electron self energy, something not previously done
in light-cone quantization and light-cone gauge.
