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

Daniel Zwanziger

doi:10.1103/PhysRevD.67.105001

paper

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

arXiv:hep-th/0206053 · doi:10.1103/PhysRevD.67.105001

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 $< W >= \int d A W P$ 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.

50 pages, 2 figures

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

Abstract

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