Anomalous Ultraviolet Divergences and Renormalizability of the Light-Cone Gauge

The one-loop renormalizability of both the two-component (LC2) and four-component (LC4) formulations of the light-cone gauge is demonstrated by construction of the complete one-loop counter Lagrangeans. The Mandelstam-Leibbrandt prescription is used to regularize the singular $\frac{1}{p^{+}}$ factor. In LC4, the one-loop self-energy and three-vertex both have anomalous, unrenormalizable ultraviolet divergences, but the counterterms associated with these divergences cancel exactly, rendering the total counter Lagrangeans for the two formulations identical, at least to $O\left(g^3\right)$.