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 this purpose, we carry out our calculations in the coordinates x^μ = (x⁺, x^-, x¹, x²), where x⁺ = x⁰ sin θ + x³ cos θ and x^- = x⁰ cos θ - x³ sin θ. Here, A_- = A⁰ cos θ + A³ sin θ = n . 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 proposed by Mandelstam and Leibbrandt. By taking the limit θ → π/4, we are able to construct a light-cone formulation that is free from infrared divergences. With that analysis complete, we next calculate the one-loop electron self-energy, something not previously done in the light-cone quantization and light-cone gauge.