Lattice QCD, O.P.E. and the Standard Model

A number of old and new methods for computing $K\to \pi \pi$ amplitudes on the lattice are reevaluated. They all involve a non-perturbative determination of matching coefficients. I will show how problems related to operator mixing can be greatly reduced by introducing the O.P.E. of hadronic currents directly on the lattice. Applications to the evaluation of CP-symmetric ($\mathrm{\Delta }I=1\mathrm{/}2$ rule) and CP-violating (${ϵ}^{\mathrm{\prime }}\mathrm{/}ϵ$) processes are presented.