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

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dc.creatorZwanziger, Daniel
dc.date2002-06-06
dc.date2003-04-18
dc.date.accessioned2026-07-07T11:10:05Z
dc.date.available2026-07-07T11:10:05Z
dc.descriptionWe 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.
dc.description50 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/hep-th/0206053
dc.identifierhttp://arxiv.org/abs/hep-th/0206053
dc.identifierPhys.Rev.D67:105001,2003
dc.identifierdoi:10.1103/PhysRevD.67.105001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190685
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Phenomenology
dc.titleTime-independant stochastic quantization, DS equations, and infrared critical exponents in QCD
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