Time-independant stochastic quantization, DS equations, and infrared critical exponents in QCD

TL;DR

This paper develops a gauge-invariant stochastic quantization method for QCD, deriving equations similar to Dyson-Schwinger equations, and non-perturbatively computes critical exponents of gluon propagators, avoiding Gribov ambiguities.

Contribution

It introduces a time-independent stochastic quantization approach based on gauge equivalence, providing a non-perturbative derivation of gluon propagator exponents in QCD.

Findings

Derived critical exponents for gluon propagators: _T \u2212 1.043 and _L .521.

Established a gauge-invariant stochastic quantization framework that avoids Gribov issues.

Compared results with Faddeev-Popov theory, highlighting differences in vertex contributions.

Abstract

We derive the equations of time-independent stochastic quantization, without reference to an unphysical 5th time, from the principle of gauge equivalence. It asserts that probability distributions $P$ that give the same expectation values for gauge-invariant observables $<W > = \int dA W P$ are physically indistiguishable. This method escapes the Gribov critique. We derive an exact system of equations that closely resembles the Dyson-Schwinger equations of Faddeev-Popov theory, which we then solve non-perturbatively for the critical exponents that characterize the asymptotic form at $k \approx 0$ of the tranverse and longitudinal parts of the gluon propagator in Landau gauge, $D^T \sim (k^2)^{-1-\a_T}$ and $D^L \sim a (k^2)^{-1-\a_L}$, and obtain $\a_T = - 2\a_L \approx - 1.043$ (short range), and $\a_L \approx 0.521$, (long range). Although the longitudinal part vanishes with the gauge parameter $a$ in the Landau gauge limit, $a \to 0$, there are vertices of order $a^{-1}$, so the longitudinal part of the gluon propagator contributes in internal lines, replacing the ghost that occurs in Faddeev-Popov theory. We compare our results with the corresponding results in Faddeev-Popov theory.