Effective descriptions of localization in a proper-time parametrized framework

TL;DR

This paper explores how proper-time formalism in relativistic quantum systems can be connected to classical observer descriptions, providing effective interpretations of localization and detection concepts.

Contribution

It introduces a restriction operation linking proper-time formalism with classical observer frameworks, enabling effective retrieval of localization and detection concepts.

Findings

Retrieves Newton-Wigner position and Kijowski time of detection concepts

Shows localization issues can be viewed as time uncertainty effects

Bridges proper-time formalism with classical measurement descriptions

Abstract

Although the quantization of relativistic systems in a proper-time framework gives new insights concerning the understanding of the so-called localization problem, classical observers cannot be treated as quantum comoving frames and real measurement are typically conceived using an external parameter related to a classical frame. Here, the connection between the proper-time formalism and usual descriptions parametrized by classical observers is obtained by defining a restriction operation that mixes contributions of different values of proper-time. Such a restriction procedure allows us to retrieve the concepts of Newton-Wigner position and Kijowski time of detection in an effective fashion, opening the possibility to interpret the related causalities issues as an apparent phenomena resulting from the time uncertainty that is inherent to every physically acceptable single-particle quantum state.