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Modelling a Particle Detector in Field Theory

By Fabio Costa A and Federico Piazza B

Abstract

The Hamiltonian of traditionally adopted (“Unruh-DeWitt”) detector models features off diagonal elements between the vacuum and the one particle states of the field to be detected. We argue that in realistic detector models the configuration “detector in its ground state + vacuum of the field ” should be an eigenstate of the Hamiltonian, because it generally corresponds to a stable bound state of the underlying fundamental theory (e.g. the ground state-hydrogen atom in a suitable QED with electrons and protons). As a concrete example, we study a local relativistic field theory where a stable particle can capture a light quantum and form a quasi-stable state. As expected, to such a stable particle correspond eigenstates of the full theory, as is shown explicitly by using a dressed particle formalism at first order in perturbation theory. We derive a model of detector (at rest) where the stable particle and the quasi-stable configurations correspond to the two internal levels, “ground ” and “excited”, of the detector. Our analysis suggests that realistic detectors have no direct access to the local field degrees of freedom. As opposed to the Unruh-DeWitt detector, our model seems to show no response when forced along an accelerated trajectory. In order to produce operationally meaningful statements, physical theories are challenged b

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