Gauge invariance and the quark-antiquark static potential

We calculate the quark-antiquark static potential to order $g^4$ in temporal-gauge quantum chromodynamics by constructing a suitably general family of gauge-invariant $q\overline{q}$ states and then selecting the one whose energy is minimal for a given $q\overline{q}$ separation $r$. Our results agree with those of conventional perturbation theory. We study various ways in which quark confinement might arise from nonperturbative effects related to the Gribov ambiguity. We find that the presence of long-range gauge fields can change the asymptotic behavior of the Coulomb Green's function from $r^{-1\mathrm{}}$ to $r^{-\frac{1}{2}}$. We illustrate this possibility by a simple example. After making some simplifying assumptions, we obtain a minimally confining potential $V\left(r\right)\mathrm{}$ that rises logarithmically for large $r$.