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 can be extracted from finite-volume correlation functions in euclidean space without analytic continuation. The K → ππ transitions and other non-leptonic decays thus become accessible to established numerical techniques in lattice QCD.