Weak transition matrix elements from finite-volume correlation functions

The two-body decay rate of a weakly decaying particle (such as the kaon) is shown to be proportional to the square of a well-defined transition matrix element in finite volume. Contrary to the physical amplitude, the latter c an be extracted from finite-volume correlation functions in euclidean space without analytic continuation. The K --> pi pi transitions and other non-l eptonic decays thus become accessible to established numerical techniques i n lattice QCD.