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 〈W〉=∫dAWP 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 k≈0 of the gluon propagator in Landau gauge. For the transverse and longitudinal parts, we find, respectively, D^T∼(k²)^-1-α_T≈(k²)^0.043, suppressed and in fact vanishing, though weakly, and D^L∼a(k²)^-1-α_L≈a(k²)^-1.521, enhanced, with α_T=-2α_L. Although the longitudinal part vanishes with the gauge parameter a in the Landau-gauge limit a⃗0 there are vertices of order a^-1 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.