W. Schleifenbaum

Infrared behavior of the ghost-gluon vertex in Landau gauge Yang-Mills theory

A semiperturbative calculation of the ghost-gluon vertex in Landau-gauge Yang-Mills theory in four and three Euclidean space-time dimensions is presented. Nonperturbative gluon and ghost propagators are employed, which have previously been calculated from a truncated set of Dyson-Schwinger equations and which are in qualitative and quantitative agreement with corresponding lattice results. Our results for the ghost-gluon vertex show only relatively small deviations from the tree-level one in agreement with recent lattice data. In particular, we do not see any sign for a singular behavior of the ghost-gluon vertex in the infrared.

Confining solution of the Dyson-Schwinger equations in Coulomb gauge

The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the Dyson-Schwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghost-gluon vertex.

Infrared analysis of propagators and vertices of Yang-Mills theory in Landau and Coulomb gauge

The infrared behavior of gluon and ghost propagators, ghost-gluon vertex, and three-gluon vertex is investigated for both the covariant Landau and the noncovariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behavior of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the Coulomb gauge.

Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

We apply a new functional perturbative approach to the calculation of the equal- time two-point correlation functions and the potential between static color charges to one-loop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schrodinger equation for the vacuum wave functional to order g 2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders.

The Ghost-Gluon Vertex in Landau Gauge Yang-Mills Theory

Possible mechanisms for gluon confinement in Yang-Mills theory in covariant gauges are discussed briefly. Implications for the infrared behavior of the Green’s functions are outlined. Results for the gluon and Faddeev-Popov ghost propagators from DysonSchwinger studies and lattice calculations are presented. The importance of the ghostgluon vertex in these studies is discussed. Numerical results for a non-perturbatively constructed ghost-gluon vertex in four and three space-time dimensions are presented.

Recent results from the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

Within the Hamiltonian approach to Yang-Mills theory in Coulomb gauge the ghost and gluon propagators are determined from a variational solution of the Yang-Mills Schroedinger equation showing both gluon and heavy quark confinement. The continuum results are in good agreement with lattice data. The ghost form factor is identified as the dielectric function of the Yang--Mills vacuum and the Gribov-Zwanziger confinement scenario is shown to imply the dual Meissner effect. The topological susceptibility is calculated.