Time-independent stochastic quantization, Dyson-Schwinger equations, and infrared critical exponents in QCD

We derive the equations of time-independent stochastic quantization, without reference to an unphysical fifth time, from the principle of gauge equivalence. It asserts that probability distributions P that give the same expectation values for gauge-invariant observables [Formula Presented] are physically indistinguishable. This method escapes the Gribov critique. We derive an exact system of equations that closely resembles the Dyson-Schwinger equations of Faddeev-Popov theory. The system is truncated and solved nonperturbatively, by means of a power law ansatz, for the critical exponents that characterize the asymptotic form at [Formula Presented] of the gluon propagator in Landau gauge. For the transverse and longitudinal parts, we find, respectively, [Formula Presented] suppressed and in fact vanishing, though weakly, and [Formula Presented] enhanced, with [Formula Presented] Although the longitudinal part vanishes with the gauge parameter a in the Landau-gauge limit [Formula Presented] there are vertices of order [Formula Presented] so, counterintuitively, the longitudinal part of the gluon propagator does contribute in internal lines in the Landau gauge, replacing the ghost that occurs in Faddeev-Popov theory. We compare our results with the corresponding results in Faddeev-Popov theory.