Relativistic Unruh-DeWitt detectors with quantized center of mass

In this paper, we extend the Unruh-DeWitt (UDW) model to include a relativistic quantized center of mass (c.m.) for detector, which traditionally has classical c.m. and follows trajectory. We develop an inertial detector following two different approaches, starting from either first- or second-quantized treatment, enables us compare fundamental differences between schemes. particular, find that notion localization is models leads distinct predictions, study by comparing spontaneous emission rates UDW interacting with massless scalar field. Furthermore, consider system in both vacuum medium our results existing describing at low energies. predictions each model, including cases, can principle be empirically distinguished, further extended optimal states processes perform such experiments. This would clarify role interactions external field differing localizations treatments.