Broken covariance of particle detector models in relativistic quantum information

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