  We study the binding energy of a heavy quark-antiquark ($q\bar{q}$) pair
using the first-order path integral formalism. This makes the Yang-Mills
constraint equation explicit, and highlights that it is valid without relying
on a semiclassical approximation. A generalized gauge-covariant Coulomb gauge
is chosen to allow for a decomposition of the chromoelectric field into a
gauge-covariant generalization of transverse and longitudinal parts. This
decomposition makes it clear that the $q\bar{q}$ binding energy is determined
solely by the solution to the constraint equation. Assuming that the low-energy
physics is dominated by the existence of a dimension-2 gluon condensate, we
develop an asymptotic series solution to the constraint equation and thus to
the $q\bar{q}$ binding energy. We predict a QCD string tension in terms of the
condensate strength and quadratic Casimir eigenvalues, and relate our result to
results coming from OPE analyses.
