Particle Detector Model Questions the Unruh Effect

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The Hamiltonian of traditionally adopted detector models features out of diagonal elements between the vacuum and the one particle states of the field to be detected. We argue that reasonably good detectors, when written in terms of fundamental fields, have a more trivial response on the vacuum. In particular, the model configuration ``detector in its ground state + vacuum of the field\' generally corresponds to a stable bound state of the underlying theory (e.g. the hydrogen atom in a suitable QED with electrons and protons) and therefore should be also an eigenstate of the model Hamiltonian. As a concrete example, we study a consistent ``fundamental\' toy field theory where a stable particle can capture a light quantum and form a quasi-stable state. To such 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 then write the corresponding Hamiltonian for a model detector (at rest) where the stable particle and the quasi-stable configurations correspond to the two internal levels, ``ground\' and ``excited\', of the detector. The accelerated version of this Hamiltonian is inevitably model dependent emph{i.e.} it will generally depend on how the stable particle/detector is forced along the accelerated trajectory. However, in its most basic version, the accelerated detector doesn\'t see Unruh radiation.