  We present a derivation of the Gribov equation for the gluon/photon Green's
function D(q). Our derivation is based on the second derivative of the
gauge-invariant quantity Tr ln D(q), which we interpret as the gauge-boson
`self-loop'. By considering the higher-order corrections to this quantity, we
are able to obtain a Gribov equation which sums the logarithmically enhanced
corrections. By solving this equation, we obtain the non-perturbative running
coupling in both QCD and QED. In the case of QCD, alpha_S has a singularity in
the space-like region corresponding to super-criticality, which is argued to be
resolved in Gribov's light-quark confinement scenario. For the QED coupling in
the UV limit, we obtain a \propto Q^2 behaviour for space-like Q^2=-q^2. This
implies the decoupling of the photon and an NJLVL-type effective theory in the
UV limit.
