The Wilson Loop in Yang-Mills Theory in the General Axial Gauge

Abstract

We test the unified-gauge formalism by computing a Wilson loop in Yang-Mills theory to one-loop order. The unified-gauge formalism is characterized by the abritrary, but fixed, four-vector $N_μ$, which collectively represents the light-cone gauge $(N^2 = 0)$, the temporal gauge $(N^2 > 0)$, the pure axial gauge $(N^2 < 0)$ and the planar gauge $(N^2 < 0)$. A novel feature of the calculation is the use of distinct sets of vectors, $\{ n_μ, n_μ^{\ast} \}$ and $\{N_μ, N_μ^{\ast}\}$, for the path and for the gauge-fixing constraint, respectively. The answer for the Wilson loop is independent of $N_μ$, and agrees numerically with the result obtained in the Feymman gauge.