Nonperturbative Landau gauge and infrared critical exponents in QCD

By D. Zwanziger. 2001

216 citations recorded by the source corpus.

We discuss Faddeev-Popov quantization at the nonperturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the nonperturbative level. The nonperturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in the Landau gauge with a cutoff at the Gribov horizon, plus a novel term that corrects for overcounting of Gribov copies inside the Gribov horizon. Nonperturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators $D(k)$ and $G(k)$ in the Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by $D(k)\ensuremath{\sim}{1/(k}^{2}{)}^{{1+a}_{D}}$ and $G(k)\ensuremath{\sim}{1/(k}^{2}{)}^{{1+a}_{G}},$ are obtained in space-time dimensions $d=2,$ 3, 4. Two possible solutions are obtained with the values, in $d=4$ dimensions, ${a}_{G}=1,$ ${a}_{D}=\ensuremath{-}2,$ or ${a}_{G}=(93\ensuremath{-}\sqrt{1201})/98\ensuremath{\approx}0.595353,$ ${a}_{D}=\ensuremath{-}{2a}_{G}.$

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/690f29e55b41c4ec1655153f5e947b0c4a48f54a

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Citations in the corpus

Nonperturbative Faddeev-Popov formula and the infrared limit of QCD (2003, background): “Recent solutions of the truncated coupled DS equations for the gluon and ghost propagators yield ghost propagators that are enhanced in the infrared, and gluon propagators that are infrared suppressed [17], [18], [19], [20], [21], [22], [23], and [3].”
QCD at finite temperature and chemical potential from Dyson–Schwinger equations (2018, background): “p 100 MeV, the DSEs can be solved analytically and exact solutions without any truncations are possible [200, 201, 266, 315, 316].”
The QCD running coupling (2016, methodology): “This dependence is verified by Lattice calculations [336, 342], the stochastic quantization approach [245], and the FRG framework [344].”
Polyakov loop modeling for hot QCD (2017, background): “Then, to capture the qualitative feature of the Polyakov loop potential in the confined phase, the so-called scaling solution should be useful, which is numerically known to behave as [68, 69, 70]”
The Infrared Behaviour of the Pure Yang–Mills Green Functions (2005, methodology): “• choice of the gauge group (SU(2) or SU(3)) Theoretical arguments lead to the conclusion that the qualitative features of the IR Green’s functions should be independent of this choice [59; 66].”
What's up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices (2007, methodology): “gime [33], in the interpolating gauge (or λ-gauge) [34] and in Coulomb gauge [35]. From the analytic point of view, it may seem necessary to reconsider partially the conventional conﬁnement scenarios [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] disc ussed in the Introduction. One should of course recall ”
The Gribov problem and QCD dynamics (2012, methodology): “1906 in Euclidean dimension d = 2,3, and 4 respectively [46].”
Nonperturbative properties of Yang–Mills theories (2018, background): “Within the available statistics, the scaling solution seemed to be realized for propagator and vertices [230, 348, 352].”