Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum

Abstract

In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2\le 0.3{\mathrm{GeV}}^2$ we find the corresponding MOM scheme running coupling ${\alpha }_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.

Comments: talk given by M. M.-P. at the Workshop on Computational Hadron Physics, Cyprus, September 2005