Broken covariance of particle detector models in relativistic quantum information

TL;DR

This paper demonstrates that spatially smeared particle detectors in relativistic quantum field theory generally lack covariance outside the pointlike limit, leading to ambiguities in time-ordering and affecting detector predictions.

Contribution

It analyzes how covariance violations depend on detector states, motion, shape, and spacetime, providing tools to evaluate and identify regimes of approximate covariance.

Findings

Covariance violations depend on detector configuration and motion.

Tools are provided to quantify the magnitude of covariance breakdown.

Certain regimes allow for approximately covariant detector predictions.

Abstract

We show that the predictions of spatially smeared particle detectors coupled to quantum fields are not generally covariant outside the pointlike limit. This lack of covariance manifests itself as an ambiguity in the time-ordering operation. We analyze how the breakdown of covariance affects typical detector models in quantum field theory such as the Unruh-DeWitt model. Specifically, we show how the violations of covariance depend on the state of the detectors-field system, the shape and state of motion of the detectors, and the spacetime geometry. Furthermore, we provide the tools to explicitly evaluate the magnitude of the violation, and identify the regimes where the predictions of smeared detectors are either exactly or approximately covariant in perturbative analyses.