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 gaugeQED in which the inherent infrared divergences are regularized by residualgauge 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 indetail that, in perturbation theory, infrared divergences resulting from theresidual gauge fields cancel infrared divergences resulting from the physicalparts of the gauge field. As a result we obtain the gauge field propagatorprescribed by Mandelstam and Leibbrandt. By taking the limit $\theta {\to}\frac{\pi}{4}$ we can construct the light-cone formulation which is free frominfrared difficulty. With that analysis complete, we perform a successfulcalculation of the one loop electron self energy, something not previously donein light-cone quantization and light-cone gauge.Comment: 29 pages; 1 figur