alpha(s) from the non-perturbatively renormalised lattice three-gluon vertex

We compute the running QCD coupling on the lattice by evaluating two-point and three-point off-shell gluon Green's functions in a fixed gauge and imposing non-perturbative renormalisation conditions on them. Our 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 range 1.8-2.3 GeV, our coupling runs according to the two-loop asymptotic formula, allowing a precise determination of the corresponding Lambda parameter, The role of lattice artifacts and finite-volume effects is carefully analysed and these appear to be under control in the momentum 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 results to the <(MS)over bar> scheme, thus eliminating a major source of uncertainty in the determination of alpha(<(MS)over bar>). Our method can be applied directly to the unquenched case. (C) 1997 Elsevier Science B.V.