Consistent histories, the quantum Zeno effect, and time of arrival

We present a decomposition of the general quantum-mechanical evolution operator that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite-dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of space-time in terms of the QZE. The comparison of the approach of consistent histories to the problem of time of arrival with the solution provided by the probability distribution of Kijowski shows the strength of the latter point of view.