Broken covariance of particle detector models in relativistic quantum information

We show that the predictions of commonly used 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, thus providing limits of validity of smeared particle detector models.