Daniel Zwanziger

Local and renormalizable action from the gribov horizon

We derive a local, renormalizable action for non-abelian gauge theories, which expresses the restriction of the domain of the functional integral to the interior of the Gribov horizon, and show that the divergences may be absorbed by field and coupling constant renormalization. The condition that the euclidean functional integral extends up to the boundary of the classical configuration space provides an absolute normalization of the gauge field and eliminates the perturbative coupling constant g2 in favor of a dimensionful parameter γ. In D = 4 dimensions, with dimensional regularization, the coupling constant g2(ϵ) is found, in zeroth order, to vanish with ϵ = 4 − D, in accordance with asymptotic freedom. In consequence of the restriction of the classical configuration space, the poles of the gluon propagator are shifted, in zeroth order, to an unphysical location at p2 = ±iγ12, but the glueball channel contains a physical cut with positive spectral function.

Nonperturbative Landau gauge and infrared critical exponents in QCD

We discuss Faddeev-Popov quantization at the nonperturbative level and show that Gribovs 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 Gribovs 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

Covariant quantization of gauge fields without Gribov ambiguity

D(k)

Fundamental modular region, Boltzmann factor and area law in lattice theory

and

Every gauge orbit passes inside the Gribov horizon

G(k)

The Gribov problem and QCD dynamics

in the Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by

Non-perturbative modification of the Faddeev-Popov formula and banishment of the naive vacuum☆

D(k)\ensuremath{\sim}{1/(k}^{2}{)}^{{1+a}_{D}}

Vanishing of zero-momentum lattice gluon propagator and color confinement

and

Action from the Gribov horizon

G(k)\ensuremath{\sim}{1/(k}^{2}{)}^{{1+a}_{G}},

Critical limit of lattice gauge theory

are obtained in space-time dimensions