Quantum states and local projective measurement in a relativistic field

In an explicitly covariant system with point-like detectors coupled to a relativistic quantum field, the Gaussian states of the combined system and the reduced states of the detectors derived from them are consistent, but not have to be covariant, in different frames of different observers. Even in the presence of spatially local projective measurements, which result instantaneous wave functional collapses on different time-slices in different reference frames, the consistency still holds.