Measurements on relativistic quantum fields: I. Probability assignment

We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of the detector. We explicitly construct the probabilities associated to $n$ measurement events, while treating the spacetime coordinates of the events are random variables. These probabilities define a linear functional of a $2n$ unequal time correlation function of the field, and thus, they are Poincar\'e covariant. The probability assignment depends on the properties of the measurement apparatuses, their state of motion, intrinsics dynamics, initial states and couplings to the measured field. For each apparatus, this information is contained in a function, the detector kernel, that enters into the probability assignment. In a companion paper, we construct the detector kernel for different types of measurement.