and this gives the time-evolution operator between time t and time t + 2 ε. While in the H representation the quantity that is being summed over the intermediate states is an obscure matrix element, in the S representation it is reinterpreted as a quantity associated to the path. In the limit that one takes a large power of this operator, one reconstructs the full quantum evolution between two states, the early one with a fixed value of q (0) and the later one with a fixed value of q (t). The result is a sum over paths with a phase, which is the quantum action.