  We discuss Faddeev-Popov quantization at the non-perturbative level and show
that Gribov's prescription of cutting off the functional integral at the Gribov
horizon does not change the Schwinger-Dyson equations, but rather resolves an
ambiguity in the solution of these equations. We note that Gribov's
prescription is not exact, and we therefore turn to the method of stochastic
quantization in its time-independent formulation, and recall the proof that it
is correct at the non-perturbative level. The non-perturbative Landau gauge is
derived as a limiting case, and it is found that it yields the Faddeev-Popov
method in Landau gauge with a cut-off at the Gribov horizon, plus a novel term
that corrects for over-counting of Gribov copies inside the Gribov horizon.
Non-perturbative but truncated coupled Schwinger-Dyson equations for the gluon
and ghost propagators $D(k)$ and $G(k)$ in Landau gauge are solved
asymptotically in the infrared region. The infrared critical exponents or
anomalous dimensions, defined by $D(k) \sim 1/(k^2)^{1 + a_D}$ and $G(k) \sim
1/(k^2)^{1 + a_G}$ are obtained in space-time dimensions $d = 2, 3, 4$. Two
possible solutions are obtained with the values, in $d = 4$ dimensions, $a_G =
1, a_D = -2$, or $ a_G = [93 - (1201)^{1/2}]/98 \approx 0.595353, a_D = -
2a_G$.
