ALPHA(S) FROM THE NON-PERTURBATIVELY RENORMALIZED LATTICE 3-GLUON VERTEX

We compute the running QCD coupling on the lattice by evaluating two-p oint and three-point off-shell gluon Green's functions in a fixed gaug e and imposing non-perturbative renormalisation conditions on them. Ou r exploratory study is performed in the quenched approximation at beta = 6.0 on 16(4) and 24(4) lattices. We show that, for momenta in the r ange 1.8-2.3 GeV, our coupling runs according to the two-loop asymptot ic formula, allowing a precise determination of the corresponding Lamb da parameter, The role of lattice artifacts and finite-volume effects is carefully analysed and these appear to be under control in the mome ntum range of interest. Our renormalisation procedure corresponds to a momentum subtraction scheme in continuum field theory, and therefore lattice perturbation theory is not needed in order to match our result s to the <(MS)over bar> scheme, thus eliminating a major source of unc ertainty in the determination of alpha(<(MS)over bar>). Our method can be applied directly to the unquenched case. (C) 1997 Elsevier Science B.V.