On a proper-time approach to localization

TL;DR

This paper introduces a proper-time formalism for relativistic quantum localization that resolves causality issues and Hegerfeldt's paradox by using covariant four-vector operators and POVM measurements.

Contribution

It develops a proper-time based single-particle formalism that is independent of external classical parameters and addresses causality concerns in relativistic localization.

Findings

Localization described by covariant four-vector operators.

Physically acceptable states require temporal uncertainty.

Proper-time evolution avoids causality violations.

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.