Abstract
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 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 of the gluon propagator in Landau gauge. For the transverse and longitudinal parts, we find, respectively, suppressed and in fact vanishing, though weakly, and enhanced, with Although the longitudinal part vanishes with the gauge parameter a in the Landau-gauge limit there are vertices of order 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.
- Received 14 June 2002
DOI:https://doi.org/10.1103/PhysRevD.67.105001
©2003 American Physical Society