### 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)

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## Cite this

*Physical Review D*,

*68*(10), [105001]. https://doi.org/10.1103/PhysRevD.68.105001