QCD perturbation theory in the temporal gauge

In this paper we present a non-trivial check of the consistency of the quantization of a gauge theory with fermions (QCD) in the temporal gauge. We use the approach based on the finite time Feynman propagation kernel, in which the Gauss law is imposed as a constraint on the states by means of a functional integration over all the time independent gauge transformations acting on the boundary values of the fields. We spell out in detail the “Feynman rules” when fermions are present and we compute, as an example, the gauge invariant correlation function $$begin{gathered} G(t) = leftlangle {bar psi (0,t)(gamma _5 gamma _0 )frac{{1 - gamma _0 }}{2}P} right. hfill left. { cdot exp left( {igintlimits_0^t {A_0 (0,t')dt'} } right)(gamma _5 gamma _0 )^ + (0,0)} rightrangle hfill end{gathered} $$ up to orderg ², obtaining the expected result.