  We propose a fully covariant model for smeared particle detectors in quantum
field theory in curved spacetimes. We show how effects related to accelerated
motion of the detector and the curvature of spacetime influence the way
different observers assign an interaction Hamiltonian between the detector and
the field. The fully covariant formulation explicitly leaves the physical
predictions of the theory invariant under general coordinate transformations,
hence providing a description of particle detector models (e.g., Unruh-DeWitt
detectors, models for the light-matter interaction, etc) that is suitable for
arbitrary trajectories in general spacetime backgrounds.
