## 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 〈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} ∼(k^{2})^{-1-αT}≈(k^{2}) ^{0.043}, suppressed and in fact vanishing, though weakly, and D ^{l}∼a(k^{2})^{-1-αL} ≈a(k ^{2})^{-1.521}, enhanced, with α_{T} = -2α_{L}. Although the longitudinal part vanishes with the gauge parameter a in the Landau-gauge limit a→0 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.

Original language | English (US) |
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Article number | 105001 |

Journal | Physical Review D |

Volume | 68 |

Issue number | 10 |

DOIs | |

State | Published - 2003 |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)