2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/88734We study the positive-operator-valued measures on the projective real line covariant with respect to the projective group, assuming that the energy is a positive operator. This problem is similar to the more complicated problem of finding the positive-operator-valued measures on the compactified Minkowski space-time covariant with respect to the conformal group. It also describes a time-of-arrival observable for a free particle covariant with respect to linear canonical transformations.21 pagesQuantum Physicstext