Quantum detection processes in quantum field theory (QFT) must play a key role in the description of quantum-field correlations, such as the appearance of entanglement, and of causal effects. We consider the detection in the case of a simple QFT model with a suitable interaction to exact treatment, consisting of a quantum scalar field coupled linearly to a classical scalar source. We then evaluate the response function to the field quanta of two-level pointlike quantum model detectors, and analyze the effects of the approximation adopted in standard detection theory. We show that the use of the RWA, which characterizes the Glauber detection model, leads in the detector response to nonlocal terms corresponding to an instantaneously spreading of source effects over the whole space. Other detector models, obtained with nonstandard or no application of RWA, give instead local responses to field quanta, apart from source-independent vacuum contribution linked to preexisting correlations of zero-point field.
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