Exploratory Study of the 3-Gluon Vertex on the Lattice

We define and evaluate on the lattice the amputated 3-gluon vertex function in momentum space. We give numerical results for ${16}^3\times 40$ and ${24}^3\times 40$ quenched lattices at $\beta =6.0$. A good numerical signal is obtained, at the price of enforcing the gauge-fixing condition with high accuracy. By comparing results from two different lattice volumes, we try to investigate the crucial issue of finite volume effects. We also outline a method for the lattice evaluation of the QCD running coupling constant as defined from the 3-gluon vertex, while being aware that a realistic calculation will require larger $\beta$ values and very high statistics.