Time of arrival and localization of relativistic particles

TL;DR

This paper develops a framework for localizing relativistic particles using time-of-arrival observables derived from quantum field interactions, addressing causality issues and linking to the Newton-Wigner position operator.

Contribution

It introduces a new approach to particle localization in relativistic QFT via time-of-arrival observables and establishes a measure of localizability based on a time-energy uncertainty relation.

Findings

Maximum localization linked to Newton-Wigner operator

Defined a measure of localizability for relativistic particles

Identified different time-of-arrival observables based on detection localization

Abstract

Constructing observables that describe the localization of relativistic particles is an important foundational problem in relativistic quantum field theory (QFT). The description of localization in terms of single-time observables leads to conflict with the requirement of causality. In this paper, we describe particle localization in terms of time-of-arrival observables, defined in terms of the interaction between a quantum field and a measuring apparatus. The resulting probabilities are linear functionals of QFT correlation functions. Specializing to the case of a scalar field, we identify several time-of-arrival observables differing on the way that the apparatus localizes particle-detection records. Maximum localization is obtained for a unique observable that is related to the Newton-Wigner position operator. Finally, we define a measure of localizability for relativistic particles in terms of a novel time-energy uncertainty relation for the variance of the time of arrival.