A study of local and non-local spatial densities in quantum field theory

TL;DR

This paper compares two methods for defining particle position in quantum field theory using a 1D model, revealing differences in localization, causality, and evolution speed.

Contribution

It introduces a comparative analysis of local and non-local spatial densities in quantum field theory, highlighting their distinct physical implications.

Findings

Newton-Wigner density allows arbitrarily narrow localization

Superluminal spreading occurs with the Newton-Wigner approach

Field operator density prevents localized states and ensures subluminal evolution

Abstract

We use a one-dimensional model system to compare the predictions of two different 'yardsticks' to compute the position of a particle from its quantum field theoretical state. Based on the first yardstick (defined by the Newton-Wigner position operator), the spatial density can be arbitrarily narrow and its time-evolution is superluminal for short time intervals. Furthermore, two spatially distant particles might be able to interact with each other outside the light cone, which is manifested by an asymmetric spreading of the spatial density. The second yardstick (defined by the quantum field operator) does not permit localized states and the time evolution is subluminal.