Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields

We study effective models describing systems of quantum particles interacting with quantized (electromagnetic) fields in the quasi-classical regime, i.e., when the field's state shows a large average number of excitations. Once the field's degrees of freedom are traced out on factorized states, the reduced dynamics of the particles' system is described by an effective Schr\"{o}dinger operator keeping track of the field's state. We prove that, under suitable assumptions on the latter, such effective models are well-posed even if the particles are point-like, that is no ultraviolet cut-off is imposed on the interaction with quantum fields.