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Quantized mass-energy effects in an Unruh-DeWitt detector

A simple but powerful particle detector model consists of a two-level system coupled to a field, where the detected particles are the field excitations. This is known as the Unruh-DeWitt detector. Research using this model has often focused on either a completely classical description of the external degrees of freedom of the detector, or a full field-theoretic treatment, where the detector itself is described as a field. Recently there has been much interest in quantum aspects of the detector's center of mass -- either described as moving in superposition along semiclassical trajectories, or dynamically evolving under a non-relativistic Hamiltonian. However, the processes of interest -- the absorption or emission of field particles -- necessarily change the detector's rest mass by the amount of energy of the absorbed or emitted field quanta. Neither of the above models can capture such effects. Here we incorporate the quantization of the detector's mass-energy into the Unruh-DeWitt model. We show that internal energy changes due to emission or absorption are relevant even in the lowest energy limit. Specifically, corrections to transition rates due to the detector's mass changing cannot be ignored unless the entire center of mass dynamics is also ignored. Our results imply that one cannot have a consistent model of the Unruh-DeWitt detector as a massive particle without including the mass-energy equivalence.