On a proper-time approach to localization

Abstract

The causality issues concerning Hegerfeldt's paradox and the localization of relativistic quantum systems are addressed through a proper-time formalism of single-particle operators. The proposed description does not depend on classical parameters connected to an external observer and results in a single-particle formalism in which localization is described by explicitly covariant four-vector operators associated with POVM measurements parametrized by the system's proper-time. As a consequence, it is shown that physically acceptable states are necessarily associated with the existence of a temporal uncertainty and their proper-time evolution is not subject to the causality violation predicted by Hegerfeldt.

7 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2009.07050