Time of ocurrence observables: expanding to other symmetries

TL;DR

This paper extends the formalism of time observables in quantum mechanics by generalizing measurement construction methods to include causal Poincaré transformations, enabling covariant measures.

Contribution

It introduces a generalized construction of time observables that are covariant under causal Poincaré transformations in quantum mechanics.

Findings

Constructed covariant time observables under Poincaré symmetry

Extended the formalism of Positive Operator Valued Measures for time measurement

Provided a framework for covariant quantum time measurements

Abstract

Recent works have proposed the use of the formalism of Positive Operator Valued Measures to describe time measurements in quantum mechanics. This work aims to expand on the work done by other authors, by generalizing the previously proposed construction method of such measures to include causal Poincar\'e transformations, in order to construct measures which are covariant with respect to such transformations.