Perturbative Formulation of Pure Space-Like Axial Gauge QED with Infrared Divergences Regularized by Residual Gauge Fields

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.